Anti-lock/traction control brake system wherein wheel brake pressure is controlled based on wheel speeds relative to vehicle speed

ABSTRACT

An apparatus for preventing excessive slipping of a wheel of a motor vehicle, including a pressure regulator for regulating a brake force for braking the wheel based on at least an amount of change of a rotating speed of the wheel, a device for obtaining the rotating speed of the wheel, a device for obtaining a running speed of the vehicle; and a device for obtaining, as a kind of the amount of change of the rotating speed of the wheel, a relative wheel speed change amount which corresponds to an amount of change of a difference between the speeds of the wheel and the vehicle.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates in general to an apparatus for preventingexcessive slipping of wheels of a motor vehicle upon acceleration orbraking of the vehicle.

2. Discussion of the Related Art

A wheel of a motor vehicle will slip on a road surface to an excessiveextent when a drive force transmitted to the wheel upon acceleration ofthe vehicle is excessive in relation to a force of friction between thewheel tire and the road surface, or when a brake force applied to thewheel upon braking of the vehicle is excessive in relation to the forceof friction between the tire and the road surface. The acceleration orbraking of the vehicle is effected in dependence on the force offriction between the wheel tire and the road surface. The force offriction is maximized when the ratio of slip of the wheel relative tothe road surface (namely, the slip amount of the wheel divided by thevehicle speed) is optimum. Accordingly, the acceleration or braking ofthe vehicle need to be effected with the slip ratio or slip amount ofthe wheel maintained in an optimum range, so that the vehicle isaccelerated or braked in a satisfactory fashion.

In view of the above need, a brake system of a motor vehicle known inthe art is adapted to effect a traction control of a wheel drive forceand/or an anti-lock control of a wheel brake force. In the wheeltraction control, a brake force is applied to a driving wheel of thevehicle to reduce an effective drive force generated by the drivingwheel, for thereby avoiding excessive slipping of the driving wheel uponacceleration of the vehicle. In the anti-lock control, the brake forceapplied to a wheel of the vehicle is reduced so as to avoid excessiveslipping of the wheel upon braking of the vehicle.

The brake force applied to the vehicle wheel as described above isregulated in various manners. An example of such manners of regulatingthe brake force is disclosed in JP-A 2-310161. According to thispublication the brake force is regulated on the basis of an amount ofchange in the rotating speed of the wheel, more specifically, on thebasis of only the amount of change in the wheel speed, or on the basisof not only the wheel speed change amount but also another parametersuch as the wheel speed per se or the vehicle speed. It is noted that anacceleration value of the wheel, which is the amount of change in thewheel speed per unit time, is considered to be a kind of the wheel speedchange amount. In the present application, however, the amount of changein the wheel speed will not be referred to as "wheel acceleration",since the amount of change in the wheel speed is treated herein as aparameter which is not necessarily an amount of change per unit time buta parameter obtained within a given time duration.

The slip amount or ratio of the vehicle wheel is calculated from thevehicle speed and the wheel speed. An amount of increase or decrease inthe wheel slip amount or ratio can be obtained from the amount of changein the wheel speed. Therefore, the slip amount or ratio of the wheel canbe maintained within the optimum range when the brake force applied tothe wheel is suitably controlled on the basis of either the wheel speed,vehicle speed and wheel speed change amount in combination, or the wheelspeed change amount alone.

Conventionally, the wheel speed change amount is detected by a suitablewheel speed sensor as an amount of change in the actual wheel speed.However, the wheel speed change amount thus obtained includes not onlyan amount of change in the wheel speed which arises from the slipping ofthe wheel on the road surface, but also an amount of change in theactual vehicle speed. Although the wheel speed change amount which doesnot include the vehicle speed change amount accurately represents achange in the slip amount or ratio of the wheel, the conventionalarrangement uses the wheel speed change amount including the vehiclespeed change amount, for regulating the brake force applied to the wheelto control the wheel slip amount or ratio.

SUMMARY OF THE INVENTION

The present invention was developed in the light of the foregoing priorart background. It is therefore an object of the present invention toprovide an apparatus for preventing excessive slipping of a wheel of amotor vehicle, which apparatus permits improved accuracy of control ofthe wheel slip amount or ratio, by utilizing a parameter which relatesto the wheel speed change amount and which accurately represents theamount of increase or decrease in the wheel slip amount or ratio.

The above object may be achieved according to the principle of thepresent invention, which provides an apparatus for preventing excessiveslipping of a wheel of a motor vehicle, including pressure regulatingmeans for regulating a brake force for braking the wheel based on atleast an amount of change of a rotating speed of the wheel, saidapparatus being characterized by comprising: (a) wheel speed obtainingmeans for obtaining the rotating speed of the wheel; (b) vehicle speedobtaining means for obtaining a running speed of the vehicle; and (c)relative speed change obtaining means for obtaining, as a kind of theamount of change of the rotating speed of the wheel, a relative wheelspeed change amount which corresponds to an amount of change of adifference between the speeds of the wheel and the vehicle obtained bythe wheel speed obtaining means and the vehicle speed obtaining means,respectively.

In the present apparatus constructed according to the invention toprevent excessive slipping of a wheel of a motor vehicle, the relativespeed change obtaining means obtains the relative wheel speed changeamount as a parameter representing the amount of change of the wheelspeed. The relative wheel speed change amount corresponds an amount ofchange of a difference between the wheel speed and the vehicle speedwhich are obtained by the wheel speed obtaining means and the vehiclespeed obtaining means, respectively.

The pressure regulating means regulates the brake force for the wheel,on the basis of at least the relative wheel speed change amount obtainedby the relative speed change obtaining means.

The relative wheel speed change amount does not include an amount ofchange of the vehicle speed, and therefore accurately represents orreflects the amount or ratio of slip of the wheel on the road surface.Since the present apparatus is arranged to regulate the brake force forthe wheel based on this relative wheel speed change amount, the slipamount or slip ratio of the wheel can be maintained within apredetermined optimum range that assures excellent acceleration and/orbraking of the vehicle.

It is desirable that at least one of the wheel speed obtaining means,vehicle speed obtaining means and relative speed change obtaining meansincorporates or is integrally combined with suitable smoothing means forsmoothing the corresponding parameter or parameters, that is, at leastone of the wheel speed, vehicle speed and relative wheel speed changeamount, so as to remove a noise from the parameter or parameters.

According to one preferred form of the present invention, the relativespeed change obtaining means includes smoothing means for obtaining asmoothed relative wheel speed change amount by smoothing the relativewheel speed change amount. According to one arrangement of this form ofthe invention, the smoothing means comprises a digital filter forobtaining the smoothed relative wheel speed change amount by digitalsmoothing of the relative wheel speed change amount. For example, thedigital filter may include a first digital filter for smoothing therelative wheel speed change amount to obtain a first relative wheelspeed change amount as the smoothed relative wheel speed change amount,and also a second digital filter for smoothing the first relative wheelspeed change amount to obtain a second relative wheel speed changeamount as the smoothed relative wheel speed change amount.

According to another arrangement of the above preferred form of theinvention, the smoothing means comprises a first digital filter forsmoothing the relative wheel speed change amount to obtain anon-compressed first relative wheel speed change amount as the smoothedrelative wheel speed change amount, and compressing means forcompressing the non-compressed first relative wheel speed change amountto obtain a compressed first relative wheel speed change amount as thesmoothed relative wheel speed change amount. The compressing means mayinclude at least one of positive compressing means and negativecompressing means. The positive compressing means is adapted to reducean absolute value of the non-compressed first relative wheel speedchange amount to obtain the compressed first relative wheel speed changeamount when the non-compressed first relative wheel speed change amountis larger than a predetermined positive value. On the other hand, thenegative compressing means is adapted to reduce the absolute value ofthe non-compressed first relative wheel speed change amount to obtainthe compressed first relative wheel speed change amount when thenon-compressed first relative wheel speed change amount is smaller thana predetermined first negative value. The present arrangement iseffective to avoid a rapid change in the compressed first relative wheelspeed change amount, which is not actually possible and which isconsidered to include a noise. Namely, the present arrangement isadapted to eliminate such noise from the non-compressed first relativewheel speed change amount when the compressed change amount is obtainedby compression of the non-compressed change amount.

In one feature of the above arrangement, the compressing means comprisesat least the negative compressing means, and the smoothing means furthercomprises means for disabling the negative compressing means when thenon-compressed first relative wheel speed change amount is smaller thana predetermined second negative value smaller than the first negativevalue. This feature is effective to avoid a delayed decrease in thebrake force upon commencement of braking of the vehicle on a roadsurface having a relatively low friction coefficient, or upon rapidlowering of the friction coefficient of the road surface.

In another feature of the same arrangement of the invention, thesmoothing means further comprises a second digital filter for smoothingthe compressed first relative wheel speed change amount obtained by thecompressing means, to obtain a second relative wheel speed change amountas the smoothed relative wheel speed change amount. According to thisfeature of the invention, the first relative wheel speed change amountis first obtained from the smoothing the initially obtained ornon-smoothed first relative wheel speed change amount, and a noisepossibly included in the smoothed first relative wheel speed changeamount is eliminated by the compressing means indicated above. Then, thecompressed first relative wheel speed change amount is further smoothedto obtain the second relative wheel speed change amount, which isconsidered to accurately represent the actual amount of change of therelative speed of the wheel with respect to the running speed of thevehicle.

According to another arrangement of the preferred form of the inventionindicated above, the smoothing means comprises at least one of thepositive compressing means and negative compressing means which havebeen described above, but does not comprise the first digital filterindicated above.

In another preferred form of the invention, which is applicable to thevehicle having a plurality of wheels, the vehicle speed obtaining meanscomprises vehicle speed estimating means for obtaining an estimatedvehicle speed on the basis of a highest wheel speed which is a highestone of the rotating speeds of the plurality of wheels.

According to one advantageous arrangement of the above form of theinvention, the vehicle speed estimating means includes means forlimiting at least one of an increasing rate and a decreasing rate of thehighest wheel speed. This arrangement permits accurate estimation of theactual running speed of the vehicle, without a noise included in theestimated vehicle speed. That is, this arrangement is based on a conceptthat an extremely rapid change in the vehicle speed takes not actuallytake place, or the rate of change in the highest wheel speed does notnormally exceed a certain limit.

According to another advantageous arrangement of the same form of theinvention, the vehicle speed estimating means includes at least one of:first adjusting means for reducing the highest wheel speed with anincrease in an external disturbance value which is common to all of theplurality of wheels; second adjusting means for increasing the highestwheel speed with a decrease in a friction coefficient of a road surfaceon which the vehicle is running; and third adjusting means for reducingthe highest wheel speed with an increase in a degree of turning of thevehicle. According to one preferred feature of this arrangement, thevehicle speed estimating means includes smoothing means for smoothingthe highest wheel speed as adjusted by at least one of the first, secondand third adjusting means, to obtain the estimated vehicle speed. Thisfeature of smoothing the highest wheel speed after its adjustment by theadjusting means indicated above is effective to minimize oscillatoryregulation of the brake force due to an excessive amount of the prioradjustment of the highest wheel speed.

According to the above preferred feature wherein the highest wheel speedis smoothed, the smoothing means may include first integrating means forobtaining a first integral by integrating an error between the estimatedvehicle speed and the highest wheel speed as adjusted by at least one ofthe first, second and third adjusting means, and second integratingmeans for obtaining a final estimated vehicle speed by integrating thefirst integral.

Where the above preferred feature of the invention is applied to theapparatus which comprises anti-lock control means for controlling thepressure regulating means to regulate the brake force for braking thewheel so as prevent excessive slipping of the wheel on a road surfaceupon braking of the vehicle, the vehicle speed estimating meanspreferably includes the above-indicated second adjusting means, and thesmoothing means preferably comprises means for setting an amount ofchange of the estimated vehicle speed upon commencement of an operationof the anti-lock control means, to a value corresponding to a frictioncoefficient of the road surface which is high enough to avoid easylocking of the wheel on the road surface. This friction coefficient ispreferably higher than 0.6, more preferably higher than 0.8, and mostpreferably almost 1.0. This arrangement assures adequate anti-lockregulation of the brake force for the wheel irrespective of whether thefriction coefficient of the road surface is relatively high or low.

The smoothing means according to the above-indicated preferred featureof the invention may comprise means for smoothing the highest wheelspeed to obtain the estimated vehicle speed such that the estimatedvehicle is more responsive to the highest wheel speed when the frictioncoefficient of the road surface decreases, than when the frictioncoefficient increases. This arrangement is based on a fact that thebraked wheel is more likely to be locked when the friction coefficientof the road surface is decreasing, than when the friction coefficient isincreasing. Alternatively, the smoothing means may comprise responseadjusting means for causing an easier change of the estimated vehiclespeed in at least one of first and second cases where the frictioncoefficient of the road surface is higher and lower than respectiveupper and lower limits, respectively, than in cases other than the firstand second cases. This arrangement assures fast and accurate estimationof the vehicle speed even when the friction coefficient of the roadsurface is extremely high or low.

The smoothing means may comprise response adjusting means for causing aneasier change of the estimated vehicle speed in at least one of firstand second cases where an error between the estimated vehicle speed andthe highest wheel speed as adjusted by at least one of the first, secondand third adjusting means is held positive and negative for more than afirst and a second predetermined time, respectively, than in cases otherthan the first and second cases. In this respect, it is noted that theerror or difference between the adjusted highest wheel speed and theestimated vehicle speed may be held positive or negative for arelatively long time if the amount of change of the estimated vehiclespeed is held relatively small for some reason or other.

Where the motor vehicle has a plurality of wheels whose brake pressuresare regulated by the pressure regulating means, and the digital filterof the smoothing means indicated above has the first and second digitalfilters as described above, the vehicle speed obtaining means maycomprise vehicle speed estimating means for obtaining an estimatedvehicle speed on the basis of a highest wheel speed which is a highestone of the rotating speed of the plurality of wheels, the vehicle speedestimating means including at least one of the first, second and thirdadjusting means described above.

In one arrangement of the above preferred arrangement, the vehicle speedestimating means comprises the first adjusting means which comprisescommon disturbance obtaining means for obtaining the externaldisturbance value on the basis of an absolute value of a smallestnegative value of the second relative wheel speed change amounts of thewheels whose brake pressures are increasing. When the second relativewheel speed change amount is positive while the brake pressure for thewheel is increasing, this generally indicates that an increase of thebrake pressure has just been commenced. The absolute value of the secondrelative wheel speed change amount during an initial period of the brakepressure increase usually accurately reflects the degree of the externaldisturbance such as waviness or bumpiness of the road surface andvibration of the wheel. In view of this fact, the largest one of theabsolute values of the second relative wheel speed change amount of thewheels is used as a parameter representing the disturbance common to allthe wheels. This arrangement minimizes an adverse influence of theexternal disturbance on the estimated vehicle speed.

The first adjusting means may further comprise means for disabling thecommon disturbance obtaining means for a predetermined time durationafter commencement of operation of the pressure regulating means toregulate the brake pressures for the wheels. During a given period aftercommencement of operation of the pressure regulating means, the amountof change of the wheel speed is relatively large, and the commonexternal disturbance value if obtained during this period usuallyincludes a considerable amount of error with respect to the actualdisturbance value. For this reason, the common disturbance obtainingmeans is disabled during the initial period of operation of the pressureregulating means. The common disturbance obtaining means may comprisemeans for limiting a decreasing rate of the disturbance value while theabsolute value of the smallest negative value is decreasing. Thisarrangement permits a relatively high response of the obtained commonexternal disturbance value to a deteriorating change of the road surfacecondition, and a relatively low response of the same to an improvingchange of the road surface condition.

The second adjusting means indicated above preferably comprises:pressure-difference generating means for generating a pressuredifference between a first rear brake pressure for one of the rear rightand left wheels whose rotating speed is higher than the other rearwheel, and a second rear brake pressure for the other rear wheel, suchthat the first rear brake pressure is lower than the second rear brakepressure; and means for increasing the highest wheel speed with anincrease in a rear wheel speed difference between the rotating speeds ofthe rear right and left wheels. This arrangement assures accuratedetermination of the vehicle speed on the basis of the higher-speed rearwheel.

The third adjusting means indicated above may comprise means forreducing the highest wheel speed with an increase in a front wheel speeddifference between the rotating speeds of the front right and leftwheels. This arrangement is based on the fact that the speed differenceof the front right and left wheels more accurately represents the degreeof turning of the vehicle, than the speed difference of the rear rightand left wheels. In this respect, it is noted that while the vehicle isturning, the load on the rear wheel on the inner side of the turningpath of the vehicle is the smallest, whereby the inner rear wheel tendsto slip on the road surface, and the rear wheel speed difference doesnot accurately represents the degree of turning of the vehicle,particularly when the pressure-difference generating means as indicatedabove is employed.

According to a further preferred form of the invention, the wheel speedobtaining means comprises: vehicle speed change calculating means forcalculating an estimated vehicle speed change amount which is adifference between two values of the running speed of the vehicle; andmeans for calculating a present value of the rotating speed of thewheel, by adding the estimated vehicle speed change amount and therelative wheel speed change amount obtained by the relative speed changeobtaining means, to a last value of the rotating speed of the wheel. Inthis case, the pressure regulating means may comprise: generating meansfor generating a reference speed of the wheel on the basis of therunning speed of the vehicle obtained by the vehicle speed obtainingmeans; and commanding means for generating a control command forregulating the brake force, on the basis of a difference between thepresent value of the rotating speed of the wheel and the reference speedof the wheel.

The present apparatus as described is suitably applicable to ananti-lock brake system comprising anti-lock control means forcontrolling the pressure regulating means to regulate the brake forcefor braking the wheel so as prevent excessive slipping of the wheel on aroad surface upon braking of the vehicle.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and optional objects, features and advantages of the presentinvention will be better understood by reading the following detaileddescription of a presently preferred embodiment of the invention, whenconsidered in connection with the accompanying drawings, in which:

FIG. 1 is a schematic view showing an anti-lock hydraulic brake systemof a motor vehicle embodying the present invention;

FIG. 2 is a schematic block diagram illustrating a hardware arrangementof an electronic control device for the brake system of FIG. 1;

FIG. 3 is a schematic block diagram illustrating a functionalarrangement of the control device of FIG. 2;

FIG. 4 is a flow chart illustrating a routine performed by means 120 ofFIG. 3 for calculating a wheel speed Vw of the vehicle and amounts ofchange ΔVw1 and ΔVw2 of the wheel speed;

FIG. 5 is a view for explaining an operation performed by the abovemeans 120 for calculating an estimated wheel speed Vext byextrapolation;

FIG. 6 is a graph for explaining compression of the first change amountΔVw1 of the wheel speed calculated by the above means 120;

FIG. 7 is a schematic block diagram illustrating a functionalarrangement of means 131 of FIG. 3 for generating an estimated vehiclespeed;

FIG. 8 is a graph for explaining calculation of estimated overshoot dropamount Prev of wheel speed by means 134 of FIG. 3;

FIG. 9 is a graph showing changes in the actual wheel speed Vw,reference wheel speed Vsn and estimated wheel speed overshoot dropamount Vprev upon abrupt change in friction coefficient μ of roadsurface during an operation of the brake system to regulate the brakepressure;

FIG. 10 is a graph for explaining a future wheel speed error "Hensaf"generated by means 122 of FIG. 3;

FIG. 11 is a graph indicating an operation to control the slip ratio ofthe rear wheels of the vehicle in the brake system of FIG. 1; and

FIG. 12 is a graph indicating an operation to control the slip ratio ofthe front wheels in the brake system of FIG. 1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring first to FIG. 1, there is shown a hydraulically operatedanti-lock brake system for a motor vehicle. In FIG. 1, reference numeral10 denotes a brake pedal connected to a master cylinder 14 through abooster 12. The master cylinder 14 is of a tandem type having twopressure chambers arranged in series. With the brake pedal 10 depressed,equal hydraulic pressures are generated as brake pressures in thepressure chambers of the master cylinder 14.

In the present hydraulic brake system, the pressure chambers of themaster cylinder 14 are connected to brakes for four wheels FR, FL, RR,RL through two mutually independent piping systems of so-called "Xarrangement". In the first piping system, one of the pressure chambersof the master cylinder 14 is connected to the brake cylinder 26 for abrake of the rear left wheel RL through a fluid passage 20, anormally-open solenoid operated valve 22 and a fluid passage 24, andalso to the brake cylinder 36 of a brake of the front right wheel FRthrough the fluid passage 20, a fluid passage 30, a normally-opensolenoid-operated valve 32 and a fluid passage 34. In the second pipingsystem, the other pressure chamber of the master cylinder 14 isconnected to the brake cylinder 46 for a brake of the front left wheelFL through a fluid passage 40, a normally-open solenoid-operated valve42 and a fluid passage 44, and also to the brake cylinder 54 for a brakeof the rear right wheel RR, through the fluid passage 40, a fluidpassage 48, a normally-open solenoid-operated valve 50 and a fluidpassage 52.

In the first piping system, the fluid passage 24 is connected to areservoir 64 through a normally-closed solenoid valve 60, while thefluid passage 34 is connected to a reservoir 64 through anormally-closed solenoid valve 62. The reservoir 64 is connected to asuction inlet of a pump 66, while an delivery outlet of the pump 66 isconnected to the fluid passage 20.

In the second piping system, on the other hand, the fluid passages 44and 52 are connected to a reservoir 72 through respectivenormally-closed solenoid valves 68 and 70. The reservoir 72 is connectedto a suction inlet of a pump 74 while a delivery outlet of the pump 74is connected to the fluid passage 40. The two pumps 66, 74 are driven bya common drive motor 76.

In the present brake system having the piping arrangement indicatedabove, therefore, the brake pressure for the rear left wheel RL, forexample, is increased when the solenoid-operated valves 22, 60 are bothplaced in their non-energized state, kept at a constant level when onlythe solenoid-operated valve 22 is placed in the energized state, anddecreased when the valves 22, 60 are both placed in the energized state.Similarly, the brake pressures for the other wheels FR, FL and RR arecontrolled. That is, an appropriate one of the pressure-increase,pressure-hold and pressure-decrease positions is selected byestablishing the corresponding combination of the operating states ofthe appropriate two solenoid-operated valves (22, 60; 32, 62; 42, 68;50, 70).

The solenoid-operated valves 22, 32, 42, 50, 60, 62, 68, 70, reservoirs64, 72, pumps 66, 74 and motor 76 constitute a major part of ananti-lock brake system actuator (hereinafter referred to as "ABSactuator") 78 indicated by a block of one-dot chain line in FIG. 1.

In the present embodiment, the brake system is adapted for use on afront-engine front-drive vehicle (FF vehicle), in which the front wheelsFR, FL are driving wheels while the rear wheels RR, RL are drivenwheels.

The ABS actuator 78 is controlled by an electronic control device 80whose major portion is constituted by a computer 82 incorporating acentral processing unit (CPU) 84, a read-only memory (ROM) 86, arandom-access memory (RAM) 88, an input interface circuit 92 and anoutput interface circuit 94, as indicated in FIG. 2. To the outputinterface circuit 94, there are connected the motor 76 and thesolenoid-operated valves 22, 32, 42, 50, 60, 62, 68 and 70 throughrespective drivers 96. To the input interface circuit 92, there areconnected wheel speed sensors 100, 102, 104, 106 and a brake switch 110through respective amplifiers 98. The wheel speed sensors 100,102, 104and 106 are adapted to detect the rotating speeds of the wheels RL, FR,FL and RR, respectively, while the brake switch 110 is turned on whenthe brake pedal 10 is depressed or operated by an operator or driver ofthe FF vehicle.

The ROM 86 stores various control programs necessary to regulate thebrake pressures to be applied to the brake cylinders 26, 36, 46, 54, inan anti-lock fashion as described below in detail. The computer 82incorporates various functional means as illustrated in the diagram ofFIG. 3, in which circles represent the wheels FL, FR, RL, RR whose brakepressures are controlled by the ABS actuator 78. The number of linesconnecting the individual functional blocks in FIG. 3 correspond to thenumber of the wheels for which the data or signals indicated by thelines are used.

The output signals of the wheel speed sensors 104, 102, 100, 106 areapplied to calculating means 120, which is adapted to calculate speedsVw of the wheels FL, FR, RL, RR and amounts of change ΔVw of the wheelspeeds Vw (more precisely, first and second relative wheel speed changeamounts ΔVw1 and ΔVw2 which will be discussed below in detail), on thebasis of the received output signals of the wheel speed sensors. Thewheel speeds Vw and first and second relative speed change amounts ΔVw1and ΔVw2 of the front wheels FL, FR which are calculated by thecalculating means 120 are applied to generating means 122 for generatingpresent and future wheel speed error values Hensa and Hensaf (which willbe described). At the same time, the calculated wheel speeds Vw of therear wheels RL, RR and relative wheel speed change amounts ΔVw1 and ΔVw2are applied to selecting means 124 for selecting one of the rear wheelsRL, RR whose speed Vw is lower than the other. The selecting means 124applies the speed Vw and change amounts ΔVw1, ΔVw2 of the selectedlower-speed rear wheel RL or RR to the generating means 122.

The computer 82 further incorporates determining means 126 fordetermining a highest one of the speeds Vw of the front and rear wheelsFL, FR, RL, RR as a maximum wheel speed Vwmax, and calculating means 128and 130 for calculating a common external disturbance value Vn0 andindividual external disturbance values Vn1, respectively. Thedisturbance value Vn0 is common to the four wheels FL, FR, RL, RR whilethe disturbance values Vn1 are specific to the respective wheels.

The computer 82 further incorporates generating means 131 for generatingan estimated vehicle speed Vve on the basis of the maximum wheel speedVwmax and the common external disturbance value Vn0, and generatingmeans 132 for generating a reference wheel speed Vsn for each of thefront wheels FL, FR and the selected lower-speed rear wheel RL or RR, onthe basis of the generated estimated vehicle speed Vve. The generatedreference wheel speed Vsn is fed to the generating means 122 indicatedabove. The generating means 122 also receives the individual externaldisturbance values Vn1 from the calculating means 130, and an estimatedovershoot drop amount vprev of the wheel speed calculated by calculatingmeans 134.

The generating means 122 is arranged to generate the present and futureerror values Hensa and Hensaf, on the basis of the received data, i.e.,wheel speeds Vw, relative wheel speed change amounts ΔVw1, ΔVw2,reference wheel speed Vsn, individual external disturbance values Vn1and overshoot drop amounts Vprev obtained for the front wheels FL, FRand the selected lower-speed rear wheel RL or RR. The computer 82 alsoincorporates determining means 136 which determines, on the basis of theerror values Hensa and Hensaf received from the generating means 122,the points of time at which the solenoid-operated values of the ABSactuator 78 are commanded to increase or decrease the brake pressuresfor the wheels FL, FR, RL, RR.

The brake pressures for the rear left and right wheels RL, RR arecontrolled in a so-called "selectro-control fashion" in which a controlcommand generated for the selected lower-speed rear wheel RL or RR isalso used for the non-selected higher-speed rear wheel, so that thepoints of time at which the brake pressure decrease is terminated differfor the selected and non-selected rear wheels RL, RR. That is, asdescribed below in detail, the point of time at which the brake pressuredecrease for the non-selected (higher-speed) rear wheel RL or RR isterminated is delayed or retarded with respect to the correspondingpoint of time for the selected (lower-speed) rear wheel RL or RR, so asto purposely reduce the slip amount of the higher-speed rear wheel forthereby increasing the speed Vw of that higher-speed rear wheel towardthe actual vehicle speed. In this sense, the non-selected orhigher-speed rear wheel is referred to as "speed monitoring wheel" whereappropriate.

Referring to the flow chart of FIG. 4, there will be described theoperation of the calculating means 120. The flow chart illustrates aroutine to be executed by the calculating means 120 at a predeterminedcycle time CYCT (e.g., 5 msec) for each of the front and rear wheels FL,FR, RL, RR.

For understanding first step S1 of the routine of FIG. 4, explanation ofthe arrangement of each wheel speed sensor 100, 102, 104, 106 indicatedabove is deemed necessary. Each wheel speed sensor (e.g., 100) includesa toothed rotor which rotates with the corresponding wheel (e.g., RL),and a stationary electromagnetic pick-up disposed in opposedrelationship with the teeth of the rotor, which has a predeterminedpitch. The pick-up is adapted to electromagnetically detect passage ofeach tooth of the rotor. The pick-up produces an output in the form of avoltage signal whose level changes during rotation of the rotor,crossing a threshold or zero level alternately upwards or downwardsbetween nominal high and low levels. With the output voltage changingwith respect to the threshold level, there is generated a pulse signalwhose rise and fall (indicated by ↑ and ↓ in FIG. 5) correspond to theedges of each tooth of the rotor of the wheel speed sensor. Further,upon occurrence of each of the rises and falls of the pulse signal, anEDGE signal is generated.

The above-indicated step S1 is provided to determine whether at leastone EDGE signal has been generated during a sampling period which isequal to the cycle time. That is, the sampling takes place at thepredetermined cycle time CYCT. An example of the sampling period isindicated in FIG. 5, as a period between the present sampling pointPRTIM and the last sampling point OLDTIM.

Normally, an affirmative decision (YES) is obtained in step S1, and thecontrol flow goes to step S2 to determine whether a time intervalbetween the last two EDGE signals is smaller than a predetermined lowerlimit or larger than a predetermined upper limit, to thereby determinewhether any abnormality associated with the EDGE signal or signals ispresent or not. Described in detail, the time interval between theadjacent EDGE signals will not change abruptly to a large extent as longas the rotor of the wheel speed sensor is rotating with thecorresponding vehicle wheel. On the other hand, an EDGE signal may notbe generated if the electromagnetic pick-up fails to detect an edge of atooth of the rotor due to an excessive amount of eccentricity of therotor, for example. Alternatively, a pseudo-EDGE signal may be generateddue to a mechanical or electric noise associated with the wheel sensor.In such events, the time interval between adjacent EDGE signals isextremely long or short as compared with that during normal operation ofthe wheel sensor. If the output voltage of the electromagnetic pick-upis excessively lowered and does not reach the threshold level duringrunning of the vehicle at a relatively low speed, an EDGE signal isabsent. In this case, too, the time interval between the adjacent EDGEsignals is longer than the predetermined upper limit. Thus, theabnormality associated with the last EDGE signal is checked in step S2depending upon the time interval between the adjacent EDGE signals oneof which is the last detected EDGE signal.

Normally, a negative decision (NO) is obtained in step S2, and step S3is implemented next. Reference is now made to FIG. 5 wherein there isshown a rectangular pulse signal which is generated based on the outputvoltage of the electromagnetic pick-up of the wheel sensor (e.g., thesensor 100). The pulse signal has rises and falls indicated by ↑ and ↓.The EDGE signals occur corresponding to these rises and falls of thepulse signal. The last two adjacent EDGE signals with respect to thepresent sampling point PRTIM were generated at points of time DTP andDTN which correspond to the last rise and fall of the pulse signal. Anaverage time length TEC of a time length DTPT between DTP and PRTIM anda time length DTNT between DTN and PRTIM is obtained asTEC=(DTPT+DTNT)/2. An average time length TECL with respect to the lastsampling point OLDTIM is similarly obtained. The last sampling pointOLDTIM is a point of time at which the affirmative decision (YES) wasobtained in the last cycle of execution of the routine of FIG. 4. StepS3 is provided to calculate a non-processed wheel speed Vxa according tothe following equations, on the basis of the average time lengths TECand TECL, and a time length CN×CYCT between the last and presentsampling points OLDTIM and PRTIM, where CN represents a natural number,which is equal to "1" in the specific example of FIG. 5.

    DVT=TECL-TEC+CN×CYCT

    Vxa=VCNV×EN/DVT

where, VCNV is a constant determined by a diameter ratio of the rotor ofthe wheel speed sensor (e.g., the sensor 100) and the correspondingwheel (e.g., rear left wheel RL), a diameter of the rotor, and the pitchof the rotor teeth, while EN represents the number of the EDGE signalsgenerated between the present sampling period between OLDTIM and PRTIM.

Normally, that is, when at least one EDGE signal is generated during thepresent sampling period, the value CN is equal to "1". If at least oneEDGE signal was not generated in the sampling period preceding the lastsampling point OLDTIM (in the last cycle n-1 of execution of the routineof FIG. 4), the value CN is "2" or a larger natural number.

It is noted that "L" as in the symbol "TECL" indicates the last cyclen-1 with respect to the present cycle n of execution of the routine ofFIG. 4. Therefore, "TECL" is the average time length TEC obtained withrespect to the last sampling point OLDTIM. This rule applies to thesymbols representing the other parameters indicated in FIG. 5.

The calculation of the non-processed wheel speed Vxa according to theabove two equations is obtained in step S3 for each of the four wheels.In practice, therefore, the following equations are used to calculatethe values Vxa of the individual wheels FL, FR, RL, RR:

    DVT(I)=TECL(I)-TEC(I)+CN(I)×CYCT

    Vxa(I) VCNV×EN(I)/DVT(I)

where, I is equal to 1, 2, 3 and 4 for the wheels FL, FR, RL and RR,respectively.

In the present embodiment, the non-processed wheel speed values Vxa arecalculated on the basis of the time interval DVT between a pointintermediate between the points of generation of the two adjacent EDGEsignals immediately preceding the present sampling point PRTIM, and apoint intermediate between the points of generation of the two adjacentEDGE signals immediately preceding the last sampling point OLDTIM,According to this arrangement, the non-processed wheel speed values Vxamay be obtained with high accuracy, even if the time interval from thepoint of generation of the EDGE signal corresponding to a rise of thepulse signal to that of the EDGE signal corresponding to a fall of thepulse signal is different from the time interval from the point ofgeneration of the EDGE signal corresponding to the fall to that of theEDGE signal corresponding to the rise, as in the example of FIG. 5,provided the rotor of the wheel speed sensor is rotating at a constantspeed.

Step S3 is followed by step S4 to calculate a non-processed wheelacceleration value DVA according to the following equations:

    DTA=(DTVL+DVT)/2

    DVA=GCNV×(Vxa-VxaL)/DTA

where, GCNV represents a constant for expressing the wheel accelerationvalue in km/hr².

Then, the control flow goes to step S5 to calculate by extrapolation anestimated wheel speed Vext at the present sampling point PRTIM, and thento step S6 to calculate the first relative wheel speed change amountΔVw1.

The estimated wheel speed Vext at the present sampling point PRTIM(namely, at each sampling point) is calculated by extrapolation on thebasis of a suitably selected number of the non-processed wheel speedvalues already obtained in step S3, on the assumption that the wheelspeed Vw will change at the same rate as in the preceding period. In thepresent example, the value Vext is calculated from the two wheel speedvalues Vxa and VxaL obtained in the present and last cycles n and n-1,according to the following equation:

    Vext=Vxa+(Vxa-VxaL)×(DVT/2+TEC)/DTA

Conventionally, the non-processed values Vxa obtained on the basis ofthe EDGE signals generated prior to the present sampling point PRTIM areused as the wheel speed at the present sampling point. Accordingly,there is some time delay (=TEC+DVT/2) between the present time and thepoint of time at which the values Vxa are effective. This time delayvaries from time to time, and this variation is one of the causes for acontrol error in regulating the brake pressures for the wheels. Further,the time delay tends to increase with a decrease in the vehicle speed.In the light of this tendency, the conventional control system inhibitsthe regulation of the brake pressures in the anti-lock fashion to avoidinadequate control of the brake pressures when the vehicle speed islower than a predetermined lower limit (e.g., 7 km/hr).

In the present embodiment, however, the wheel speed values Vext for thewheels are estimated at each sampling point (at the present samplingpoint) at the predetermined cycle time CYCT, whereby the brake pressurescan be regulated with adequate timings of commencing and terminating thepressure decrease without a delay. This feature cooperates with theother features (described below) of the present embodiment to permitoptimum anti-lock control of the brake pressures even at a vehicle speedlower than7 km/hr, for example.

The calculation of the first relative wheel speed change amount ΔVw1 instep S6 is effected on the basis of the following values: a smoothedwheel speed Vw obtained in step S14 in the last cycle n-1; the estimatedwheel speed Vext obtained in step S5 in the present cycle n; anestimated vehicle speed change amount ΔVve obtained in the last cyclen-1; and a compressed value of the first change amount ΔVw1 in the lastcycle n-1. The meaning of "compression" of the first change amount ΔVw1will become apparent from the following description.

To calculate the present first relative wheel speed change amount ΔVw1,a pre-compressed first change amount ΔVwx1 is initially calculatedaccording to the following equation.

    Vtmp=Vw.sub.n-1 +ΔVve

    ΔVwx1.sub.n =ΔVw1.sub.n-1 ×C1+(Vext-Vtmp)×C2

    C1=1-2×C2

In the present embodiment, C1 is 0.5 while C2 is 0.25. The values withthe subscript "n" and "n-1" in the above equations are values obtainedin the present and last cycles, respectively. The estimated vehiclespeed change amount ΔVve is an amount of change of the estimated vehiclespeed Vve (which will be explained) during the cycle time CYCT.

The above value Vext-Vtmp is equal to (Vext-Vw_(n-1))-ΔVve, whichcorresponds to an amount of change of the present value (obtained in thepresent cycle n) of the wheel speed (relative wheel speed Vwv) relativeto the estimated vehicle speed Vve, from the preceding value obtained inthe last cycle n-1. Namely, the value (Vext-Vw_(n-1))-ΔVve is an amountof change of a difference (Vw-Vve) between the wheel speed Vw and theestimated vehicle speed Vve, more precisely, an amount of change of thepresent value of the difference (Vw-Vve) with respect to the last value(obtained in the last cycle). The pre-compressed first relative wheelspeed change amount ΔVwx1 is an incomplete integral of the above-definedamount of change of the relative wheel speed Vwv or difference (Vw-Vve),which is referred to as a first integral as distinguished from a secondintegral which will be described.

The pre-compressed first change amount ΔVwx1 is then compressed toobtain the compressed first relative wheel speed change amount ΔVw1,according to the following equations and as shown in the graph of FIG.6. ##EQU1## where, C3=0.525, C4=-0.35, C5=0.125 C6=-2.1

It will be understood from the graph of FIG. 6 that the "compression" ofthe pre-compressed change amount ΔVwx1 into the compressed firstrelative wheel speed change amount ΔVw1 takes place where thepre-compressed value ΔVwx1 is larger than a predetermined upper limit C3or smaller than a predetermined lower limit C4. This compression isbased on an assumption that the pre-compressed value ΔVwx1 outside arange defined by the upper and lower limits C3, C4 includes a noise, andthat this noise should be eliminated by the compression. Namely, theconversion of the pre-compressed value ΔVwx1 into the compressed valueΔVw1 is based on an assumption that an excessive rate of change of therelative wheel speed Vwv as expressed by the pre-compressed value ΔVwx1larger than the upper limit C3 or smaller than the lower limit C4 wouldnot occur during normal running of the vehicle on an ordinary roadsurface.

However, such excessive rate of change may occur when the vehicle isbraked on a road surface having a considerably low friction coefficientμ or when the friction coefficient μ of the road surface is suddenlylowered. In this event, the pre-compressed change amount ΔVwx1 may besmaller than a predetermined second lower limit C4+C6. To avoid delayedreduction in the brake pressures for the wheels FL, FR, RL, RR in suchevent, the pre-compressed value ΔVwx1 smaller than that lower limitC4+C6 is not compressed as indicated in the graph of FIG. 6.

The compressed first relative wheel speed change amount ΔVw1 thusobtained from the pre-compressed first change amount ΔVwx1 generated inthe last cycle n-1 is used as the first relative wheel speed changeamount ΔVw1 in the present cycle n. The "first change amount ΔVw1" ishereafter interpreted to mean the first relative wheel speed changeamount compressed according to the predetermined relationship betweenΔVw1 and ΔVwx1 as described above.

The upper and lower limits C3, C4 and C6 are expressed in unit ofkm/hr/5 msec, and the above-specified values of these limits C3, C4 andC6 are equivalent to 3 G, -2 G and -12 G, respectively, where Grepresents gravitational acceleration unit. The upper limit C3 of 3 Gand the lower limit C4 of -2 G define a permissible range ofacceleration and deceleration of the vehicle during running on a roadsurface having a relatively good condition (having sufficiently highfriction coefficient). A deceleration value of the vehicle lower thanthe lower limit (C4+C6) of -14 G (=-2 G-12 G) means that the frictioncoefficient μ of the road surface is excessively low, causing easylocking of the vehicle wheels. In this case, the first relative wheelspeed change amount ΔVw1 is obtained without compression of thepre-compressed value ΔVwx1.

Thus, the first change amount ΔVw1 of the relative wheel speed Vwv isdetermined to control the brake pressures so as to meet various roadsurface conditions, namely, both good and bad road surfaces havingdifferent values of friction coefficient μ.

As indicated above, the relative wheel speed Vwv indicated above isexpressed by the following equation:

    Vwv=Vw-Vve

On the other hand, the present wheel speed error value Hensa generatedby the generating means 122 as described below in detail is expressed bythe following equation:

    Hensa=Vw-Vsn

Since the amounts of change during the cycle time CYCT of the estimatedvehicle speed Vve and the reference wheel speed Vsn generated by thegenerating means 132 as described below in detail are substantiallyequal to each other, an amount of change ΔVwv (=ΔVw1) of the relativewheel speed Vwv is substantially equal to an amount of change ΔHensa ofthe present wheel speed error value Hensa.

The first relative wheel speed change amount ΔVw1 (=ΔVwv) is defined bythe following equation:

    ΔVw1.sub.n ΔVwv.sub.n =(Vw-Vve).sub.n -(Vw-Vve).sub.n-1 =(Vw-Vsn).sub.n -(Vw-Vsn).sub.n-1

It will thus be understood that the first change amount ΔVw1 which isthe amount of change ΔVwv of the relative wheel speed Vwv (=differenceVw-Vve) is equal to the amount of change ΔHensa of the present wheelspeed error value Hensa.

The relative wheel speed Vwv may be considered to be an error value ofthe wheel speed Vw. By effecting a filtering operation to remove thiserror component, the first relative wheel speed change amount ΔVw1 canbe correctly obtained, in spite of an error included in the absolutevalue of the estimated vehicle speed Vve, provided that the gradient ofthe value Vve is correct.

Further, by using the non-processed estimated wheel speed Vext as aninput to the digital filter for the first relative wheel speed changeamount ΔVw1, it is possible to avoid an error of quantization of thewheel acceleration value (i.e., first relative wheel speed change amountΔVw1). As is apparent from the following explanation, therefore, thefilter for the wheel speed may also serve as a digital filter for thewheel acceleration, which filter is conventionally required in additionto the filter for the wheel speed.

Referring back to step S1, the control flow goes to step S7 if anegative decision (NO) is obtained in step S1, namely, if at least oneEDGE signal has not been generated during the present sampling period(between PRTIM and OLDTIM). Step S7 is implemented to determine whethereach wheel of the vehicle is in a locked state (state of skidding on theroad surface) or not. This determination is effected by checking if apredetermined time T1 (e.g., 55 msec) has passed after the moment ofgeneration of the last normal EDGE signal (rise or fall of the pulsesignal based on the output of the wheel speed sensor 100, 102, 104,106). If the predetermined time T1 has not expired yet, this means thatthe wheel in question is not being locked. If the time T1 has alreadyexpired (before the present sampling point PRTIM), this means thelocking of the wheel.

If the negative decision (NO) is obtained in step S7, steps S3 throughS6 are not implemented, and the non-processed estimated wheel speed Vextand the first relative wheel speed change amount ΔVw1 are not updated inthe present cycle n. Consequently, the last calculated first relativewheel speed change amount ΔVw1 remains effective if the wheel is notlocking.

However, it is possible to calculate by extrapolation the presentnon-processed estimated wheel speed Vext according to the followingequation including the cycle time CYCT, to update the first changeamount ΔVw1, even when any EDGE signal has been generated during thepresent sampling period.

    Vext=Vext+(Vxa-VxaL)×CYCT/DTA

If the affirmative decision (YES) is obtained in step S7, the controlflow goes to step S9 to zero the currently effective non-processedestimated wheel speed Vext and first relative wheel speed change amountΔVw1.

If any abnormality associated with the EDGE signal or signals is foundin step S2, step S10 is implemented to determine whether the abnormalityis of a simple nature or not, that is, whether the abnormality is themissing of an EDGE signal or signals which should have been generated,or the generation of a pseudo-EDGE signal or signals which should nothave been generated. In other words, the abnormality of a simple naturecan be dealt with by adding the missing EDGE signal or signals or byeliminating the pseudo-EDGE signal or signals. If an affirmativedecision (YES) is obtained in step S10, step S11 is implemented to addor eliminate the EDGE signal or signals which caused the abnormality.Step S11 is followed by step S3 and the subsequent steps. If a negativedecision (NO) is obtained in step S10, that is, if the abnormality isnot of a simple nature, the control flow goes to step S12 to firstcalculate an estimated number of the EDGE signals (during the presentsampling period) which represents the present wheel speed Vw_(n) that isclosest to the last wheel speed Vw_(n-1) but is lower than the maximumwheel speed Vwmax (determined in the last cycle n-1 by the determiningmeans 126 as described below in detail). Then, in step S12, adifferential number of the EDGE signals is calculated by subtracting theactual number of the EDGE signals (generated during the sampling period)from the calculated estimated number of the EDGE signals.

Step S12 is followed by step S13 to determine whether the differentialnumber of the EDGE signals obtained in step S12 is an odd number or not.Normally, a pair of EDGE signals are generated corresponding to a riseand a fall of the pulse signal, that is, corresponding to upward anddownward zero-crossings of the output voltage of the electromagneticpick-up of the wheel speed sensor, for each peak of the output voltage.Therefore, the number of the EDGE signals normally generated during eachsampling period is even. Accordingly, only when a negative decision (NO)is obtained in step S13, steps S3 through S6 are implemented withrespect to the estimated number of the EDGE signals obtained in stepS12, namely, with the actually detected number of the EDGE signals beingchanged by the compensated number also obtained in step S12. If thecompensated number of the EDGE signals obtained in step S12 is odd, thismeans the missing of an EDGE signal due to some abnormality, andtherefore steps S3 through S6 are not implemented. In this case, thenon-processed estimated wheel speed Vext is not updated, for example.The determination in step S13 is effected by determining whether anequality 2 m-1<compensated number of the EDGE signals <2 m+1 (where m isan integer) is satisfied or not.

After step S6 is completed or when the negative decision (YES) isobtained in step S13, the control flow goes to step S14 to calculate thesmoothed wheel speed Vw. The calculation of the smoothed wheel speed Vwis effected according to the following equation, on the basis of thefirst relative wheel speed change amount ΔVw1_(n) obtained in step S6 ofthe present cycle n, the smoothed wheel speed Vw_(n-1) obtained in stepS14 in the last cycle n-1 and an amount of change ΔVve of the estimatedvehicle speed Vve.

    Vw.sub.n =Vw.sub.n-1 +ΔVve+ΔVw1.sub.n =Vtmp+ΔVw1.sub.n

Thus, the smoothed wheel speed Vw is calculated by integrating the firstrelative wheel speed change amount ΔVw1 and the change amount ΔVve ofthe estimated wheel speed Vve, and is referred to as the secondintegral.

It will be understood that the smoothed wheel speed Vw is obtained onthe basis of the above-indicated second integral which is based on thefirst integral indicated above. Further, the smoothed wheel speed Vw isfree from the noise owing to the "compression" of the pre-compressedfirst change amount ΔVwx1 into the compressed value ΔVw1. It will alsobe understood that the portion of the computer 82 assigned to calculatethe first relative wheel speed change amount ΔVw1 and smoothed wheelspeed Vw serves as the filter for filtering the wheel speed and thewheel acceleration value (amount of change of the relative wheel speed).

Step S14 is followed by step S15 in which the second amount of changeΔVw2 of the relative wheel speed Vwv during a 40 msec period iscalculated on the basis of the first relative wheel speed change amountΔVw1, according to the following equation:

    ΔVw2.sub.n =ΔVw2.sub.n-1 ×7/8+ΔVw1

The second relative wheel speed change amount ΔVw2 is an integral of thefirst relative wheel speed change amount ΔVw1 during the 40 msec period,that is, during a period eight times as long as the cycle time CYCT (5msec in this embodiment). Accordingly, the second relative wheel speedchange amount ΔVw2 may be calculated by summing the eight values of thefirst relative wheel speed change amount ΔVw1 obtained in the last eightsampling periods. This calculation, however, requires storing the lasteight values of the first change amount ΔVw1. To reduce the requiredmemory capacity of the computer 82, the present embodiment is adapted tocalculate the second relative wheel speed change amount ΔVw2 accordingto the above equation.

Alternatively, the second relative wheel speed change amount ΔVw2 may becalculated by obtaining a weighted mean of the pre-compressed firstchange amount ΔVwx1 and the compressed first relative wheel speed changeamount ΔVw1 according to the following equations:

    Tmp=ΔVwx1.sub.n ×0.25+ΔVw1.sub.n ×0.75

    ΔVW2.sub.n =ΔVw2.sub.n-1 ×7/8+Tmp

The calculating means 120 is adapted to execute the routine of FIG. 4for each of the four wheels FL, FR, RL and RR, whereby the four valuesof the smoothed wheel speed Vw and the four values of the first andsecond relative wheel speed change amounts ΔVw1 and ΔVw2 are obtainedfor the respective four wheels.

The smoothed wheel speed Vw will be hereinafter referred to simply aswheel speed Vw, unless the adjective "smoothed" is necessary for somereason or other. Symbols Vwfl, Vwfr, Vwrl and Vwrr will be used torepresent the speeds of the wheels FL, FR, RL and RR, respectively.

The wheel speeds Vwfl, Vwfr, Vwrl and Vwrr are fed to the determiningmeans 126, which determines the highest one of these wheel speeds as themaximum wheel speed Vwmax.

The present brake system is designed so that the amounts of slip of therear wheels RL, RR under braking are smaller than those of the frontwheels FL, FR, as long as the friction coefficient μ of the road surfaceis held almost uniform for the four wheels (in particular, almost equalfor the front and rear wheels). Consequently, one of the rear wheelspeeds Vwrl and Vwrr is the highest of the four wheel speeds. That is, ahigher one of the rear wheel speeds Vwrl and Vwrr is determined as themaximum wheel speed Vwmax.

The four values of the second relative wheel speed change amounts ΔVw2of the four wheels, which are calculated by the calculating means 120,are applied to the disturbance calculating means 128 and 130 forcalculating the common and individual external disturbance values Vn0and Vn1, respectively.

As indicated above, the relative wheel speed Vwv is considered to be anerror of the wheel speed Vw, and the amount of change ΔVw1 of therelative wheel speed Vwv is the first relative wheel speed change amountΔVw1. Therefore, the second change amount ΔVw2 obtained by integratingthe first change amount ΔVw1 may also be considered as an amount ofchange of the relative wheel speed Vwv. The second relative wheel speedchange amount ΔVw2 increases with an increase in the externaldisturbance values which result from the waviness or bumpiness of theroad surface and the vibrations of the wheels, for example. Accordingly,the external disturbances may be estimated from the second amount ofchange ΔVw2 of the relative wheel speed Vwv.

The calculating means 128 for calculating the common externaldisturbance value Vn0 receives from the determining means 136 data (notshown in FIG. 3) indicating that a predetermined time (e.g., 40 msec)has passed after commencement of regulation of the brake pressures inthe brake cylinders 26, 36, 46, 54, and data (not shown in FIG. 3)indicative of the brake cylinder or cylinders whose brake pressure is inthe process of increasing. After this predetermined time has passedafter the commencement of regulation of the brake pressures, thecalculating means 128 selects, as a minimum value ΔVw2min (negativevalue), the smallest one of the values of the second relative wheelspeed change amount ΔVw2 of the wheels corresponding to the brakecylinders whose brake pressures are increasing. The calculating means128 then calculates the common external disturbance value Vn0 on thebasis of the minimum value ΔVw2min according to the following equations:##EQU2##

The constant or gain C8 is a square root of 1/2. The gain C8 should besufficiently small to assure sufficient stability of regulation of thebrake pressures, since the common external disturbance value Vn0 isbased on the minimum value ΔVw2min which is the smallest one of the fourvalues of the second relative wheel speed change amount ΔVw2 of the fourwheels.

The above equation Vn0=MAX(Vn0-C7, -Tmp×C8) is formulated so that thecommon external disturbance value Vn0 increases with an increase in theabsolute value |ΔVw2min|, and so that the rate of decrease in the valueVn0 with a decrease in the absolute value |ΔVw2min| does not exceedC7/CYCT.

The common external disturbance value Vn0, which is the magnitude of theexternal disturbance common to all the four wheels FL, FR, RL and RR, isobtained according to the above equation so that the value Vn0 changesat a comparatively high rate while the road surface condition isdeteriorated, and at a comparatively low rate while the road surfacecondition is improved. The disturbance value Vn0 is relatively highlyresponsive to disturbances (e.g., bumpiness of the road surface) whosemagnitude changes in a comparatively large degree at a comparatively lowfrequency, which disturbances result, for example, from a road surfacewhose waviness or bumpiness slowly changes in a comparatively largeamount.

The calculating means 130 calculates the individual disturbance valuesVn1 of the wheels by smoothing the positive values of the secondrelative wheel speed change amount ΔVw2 of the front wheels FL, FR andthe selected lower-speed rear wheel RL or RR, according to the followingequation:

    Vn1=Vn1+{MAX(0,ΔVw2×C9-Vn1)}/20

The disturbance values Vn1 are specific to the individual wheels, andchange at a relatively high rate, being relatively highly responsive todisturbances whose magnitude changes in a comparatively large degree ata comparatively high frequency. These disturbances result, for example,from vibrations of the wheels.

The generating means 131 generates the estimated vehicle speed Vve, onthe basis of the common disturbance value Vn0 obtained by thecalculating means 128 and the maximum wheel speed Vwmax obtained by thedetermining means 126.

The generating means 131 has various functional means as illustrated inthe block diagram of FIG. 7, which includes calculating means 140 foreventually obtaining the estimated vehicle speed Vve.

The calculating means 140 receives: maximum wheel speed Vwmax obtainedby the determining means 126; common disturbance value Vn0 obtained bythe calculating means 128; absolute value of a rear wheel speeddifference Vwrdif obtained by calculating means 144; and absolute valueof a front wheel speed difference Vwfdif obtained by calculating means146, which difference Vwfdif represents an amount of turning of thevehicle.

As described below in detail, the present embodiment is arranged so thatthe estimated vehicle speed Vve is lowered with an increase in thecommon external disturbance value Vn0 (obtained depending upon theamounts of change in the speeds of the four wheels), in order to raisethe brake pressures during running of the vehicle on a relatively badroad surface, namely, in order to improve the operating characteristicsof the brake system while the road surface condition is relatively bad.

Further, the brake pressure of the brake cylinder 26 or 54 of thenon-selected higher-speed rear wheel RL or RR is purposely lowered withrespect to the brake pressure for the lower-speed rear wheel, asindicated above, so that the higher-speed rear wheel is used as thespeed monitoring wheel. This arrangement causes the rear wheel speeddifference Vwrdif to increase with a decrease in the frictioncoefficient μ of the road surface. Accordingly, the estimated vehiclespeed Vve obtained by the calculating means 140 is raised with anincrease in the absolute value |Vwrdif| (rear wheel speed difference),thereby improving the operating characteristics of the brake system whenthe friction coefficient μ of the road surface is low.

On the other hand, the use of the speed Vwrl or Vwrr of the higher-speedrear wheel RL or RRmay cause early reduction in the brake pressuresduring turning of the vehicle, resulting in insufficient braking forcesapplied to the wheels. To avoid this drawback, the degree of turning ofthe vehicle is detected on the basis of the absolute value |Vwfdif| ofthe front wheels FL, FR, and the estimated vehicle speed Vve is loweredwith an increase in the detected degree of turning of the vehicle.

The calculating means 144 calculates the absolute value of the rearwheel speed difference Vwrdif on the basis of a smoothed rear wheelspeed difference Vwrdif1 received from calculating means 148, and areference rear wheel speed difference Vwrdif0 received from generatingmeans 150.

The calculating means 148 calculates the smoothed rear wheel speeddifference Vwrdif1, as indicated below. ##EQU3##

The error value Tmp in the above equations is an error of the rear wheelspeed difference (Vwrr-Vwrl) from the smoothed rear wheel speeddifference Vwrdif1_(n-1) in the last cycle n-1. When the error value Tmpis a positive Vwrdif1_(n) (obtained in the present cycle n) iscalculated by value, the present smoothed rear wheel speed differenceadding the last smoothed rear wheel speed difference Vwrdif1_(n-1) to asmaller one of the error value Tmp and a limit value Eps1. When theerror value Tmp is zero or a negative value, the present valueVwrdif1_(n) is calculated by adding the last value Vwrdif1_(n-1) to alarger one of the error value Tmp and a limit value -Eps1. That is, thesmoothed rear wheel speed difference Vwrdif1, which is a differencebetween the speeds of the rear wheels RR and RL, is determined so as tolimit a rate of change of the rear wheel speed difference to within theabsolute value |Eps1|, irrespective of whether the difference increasesor decreases. The limit value Eps1 is 0.07 km/hr, for example.

The generating means 150 generates the reference rear wheel speeddifference Vwrdif0, by calculation according to the following equation:

    Vwrdif0=Vve×0.02+0.5

where, Vve is the estimated vehicle speed Vve obtained by thecalculating means 140 in the last cycle n-1.

The generating means 144 generates the absolute value of the rear wheelspeed difference Vwrdif, as indicated below, on the basis of thesmoothed rear wheel speed difference Vwrdif1 and the reference rearwheel speed difference Vwrdif0 which have been obtained as describedabove. ##EQU4##

The value ABS(Vwrdif1) in the above equation represents an absolutevalue of the smoothed rear wheel speed difference Vwrdif1, whichabsolute value is positive irrespective of which one of the speeds ofthe rear wheels RR and RL is higher. The error value Tmp is an error ofa difference between the absolute value of the smoothed rear wheel speeddifference Vwrdif1 and the reference rear wheel speed differenceVwrdif0, from the absolute value of the last rear wheel speed differenceVwrdif_(n-1). The absolute value |Vwrdif| represents a differencebetween the absolute value of the smoothed rear wheel speed differenceVwrdif1 and the reference rear wheel speed difference Vwrdif0. Like thesmoothed rear wheel speed difference Vwrdif1, the absolute value of therear wheel speed difference Vwrdif is determined so that the rate ofchange of this value Vwrdif does not exceed the limit value |Eps2|,which is 0.07 km/hr, for instance.

The calculating means 146 calculates the absolute value of the frontwheel speed difference Vwfdif, on the basis of a smoothed front wheelspeed difference Vwrdif1 received from calculating means 152, and amaximum front wheel speed difference Vwrdifmax received from calculatingmeans 154.

The calculating means 152 calculates the smoothed front wheel speeddifference Vwfdif1, as indicated below. ##EQU5##

The calculating means 146 calculates the absolute value of the frontwheel speed difference Vwfdif according to the following equations:

    Vwfdif=ABS(Vwfdif1)×K2

    Vwfdif=MAX(Vwfdif, Vwfdifmax)

The value K2 is an adjusting constant selected within a range between0.5 and 0.75. In the present embodiment, the constant K2 is equal to0.75. The meaning of this constant K2 will be explained.

If the absolute value of the front wheel speed difference Vwfdifcalculated by the calculating means 146 exceeds the maximum front wheelspeed difference Vwfdifmax calculated by the calculating means 154, thevalue Vwfdifmax is used as the absolute value of the front wheel speeddifference Vwfdif.

The maximum front wheel speed difference Vwfdifmax is a value whichcannot be smaller in theory than the front wheel speed differenceVwfdif, and is calculated according to the following equation:

    Vwfdifmax=1.3×0.5×9.8×3.6.sup.2 /Vve

The above equation is formulated with the following taken intoconsideration:

A lateral acceleration Gy of the vehicle, a radius R of turning of thevehicle and the estimated vehicle speed Vve have a relationship Gy=Vve²/R. Further, the turning radius R, the estimated vehicle speed Vve, adistance Ww between the front wheels FL and FR, and the front wheelspeed difference Vwfdif have a relationship Vwfdif=Vve×Ww/R. Therefore,an equation Vwfdif=Ww×Gy/Vve is obtained. It is empirically known thatthe maximum lateral acceleration Gy of the vehicle during running on aroad surface having a sufficiently high friction coefficient μ is in arange of 0.5-0.6 G. The above equation Vwfdifmax=1.3×0.5×9.8×3.6² /Vveis obtained by substituting 0.5 G and 1.3 m for Gy and Ww, respectively,in the above equation Vwfdif=Ww×Gy/Vve, and expressing Vwfdif(=Vwfdifmax) in unit of km/hr.

The calculating means 140 first obtains the maximum wheel speed Vwmax bylimiting the non-processed maximum wheel speed vwxmax as received fromthe determining means 126, according to the following equations:

    Vwxmax=Max(Vwfr, Vwfl, Vwrr, Vwrl)

    Tmp=Min(Vwmax.sub.n-1 +0.175, Vwxmax)

    Vwmax.sub.n =Min(Vwmax.sub.n-1 -0.35, Tmp)

As indicated above, the amount of increase in the maximum wheel speedVwmax during the 5 msec sampling period is limited to 0.175 km/hr, whilethe amount of decrease in the maximum wheel speed Vwmax during thesampling period is limited to -0.35 km/hr. The limit values 0.175 km/hrand -0.35 km/hr during the 5 msec sampling period are equivalent to 1 Gand -2 G, respectively.

Then, a compensated maximum wheel speed Vwmaxc is calculated accordingto the following equation:

    Vwmaxc=vwmax-Vn0+Vwrdif×K1-Vwfdif×K2

However, the value (Vwfdif×K2) is used to obtain the compensated maximumwheel speed Vwmaxc only when the absolute value of the front wheel speeddifference Vwfdif exceeds a threshold value for more than apredetermined length of time, that is, only when the vehicle is turning.

The compensated maximum wheel speed Vwmaxc decreases with an increase inthe common external disturbance value Vn0 (positive value), which isobtained by the calculating means 128 as described above. Thisarrangement is effective to avoid excessive reduction in the brakepressures during running of the vehicle on a bad road surface.

The value K1 is a value for adjusting the smoothed rear wheel speeddifference Vwrdif1, so as to avoid an excessive increase in the brakepressures due to an excessive amount of slip of the higher-speed rearwheel (which is the highest-speed wheel of all the four wheels) when thefriction coefficient μ of the road surface is considerably low. In otherwords, even the highest-speed rear wheel slips on the road surface to aconsiderable extent if the friction coefficient of the road surface isexcessively low. In this case, the amount of slip of that highest-speedrear wheel is not detected and will result in increasing the brakepressures to unnecessarily high levels. To avoid such drawback, theadjusting value K1 is used for reducing the smoothed rear wheel speeddifference Vwrdif1. This value K1 is selected within a range of0.125-0.25. In the present embodiment, the value K1 is set at 0.25.

On the other hand, the value K2 is a value for adjusting the smoothedfront wheel speed difference Vwfdif1, with the degree of turning of thevehicle taken into account. In this respect, it is noted that the frontwheel speed difference increases with an increase in the angularvelocity of the vehicle due to the vehicle turning. The adjusting valueK2 is provided to lower the compensated maximum wheel speed Vwmaxc asthe absolute value of the front wheel speed difference Vwfdif increases.

Theoretically, the adjusting value K2 for adjusting the front wheelspeed difference in relation to the vehicle turning should be 0.5.However, since the rear wheel speed difference is also influenced by theturning of the vehicle, this aspect should be taken into considerationin determining the adjusting value K2. In the present embodiment, theadjusting value K2 is set at (K1+0.5)=0.75, which offsets the adjustmentby the adjusting value K1 in connection with the rear wheel speeddifference Vwrdif.

It is noted that the individual external disturbance value Vn1 iscalculated on the basis of a positive value of the second relative wheelspeed change amount ΔVw2, while the common external disturbance valueVn0 is calculated on the basis of a negative value of the secondrelative wheel speed change amount ΔVw2. According to this arrangement,the maximum wheel speed Vwmaxc compensated by positive feedback does notsuffer from oscillation, whereby the response and stability of thecompensated maximum wheel speed Vwmaxc are improved.

In view of the fact that the vehicle turning has an influence on therear wheel speed difference, it is possible to adjust the absolute valueof the rear wheel speed difference Vwrdif depending upon the degree ofthe vehicle turning, rather than the front wheel speed difference.However, it is noted that one of the right and left rear wheels which ison the inner side with respect to the turning path of the vehicle hasthe smallest load, and consequently tends to have a comparatively largeamount of slip. This means that the front wheel speed differencereflects the angular velocity of the vehicle more accurately than therear wheel speed difference during turning of the vehicle. For thisreason, the front wheel speed difference Vwfdif is adjusted by theadjusting value K2 depending upon the angular velocity.

The generating means 131 calculates the estimated vehicle speed Vve onthe basis of the thus compensated maximum wheel speed Vwmaxc. Moreprecisely, an amount of change ΔVve of the estimated vehicle speed isobtained as a first integral of an error Error between the compensatedVwmaxc and the estimated vehicle speed Vve, and the estimated vehiclespeed Vve is obtained as a second integral of the error value Error.

The first integral ΔVve (amount of change of the estimated vehicle speedduring the sampling period=cycle time CYCT) is proportional to thefriction coefficient μ between the road surface and the tires of thewheels, if the brake pressures for the wheels are properly controlled.Where the road surface condition is almost constant, the amount ofchange ΔVve is expected to be almost constant. In this sense, it isdesirable that the amount of change ΔVve be moderately or slowlyadjusted.

During an initial period immediately after commencement of brakepressure regulation, or when the friction coefficient μ of the roadsurface changes from a relatively high value to a relatively low value,it is desirable that the amount of change ΔVve be adjusted at asufficiently early point of time with respect to the rate of change ofthe friction coefficient.

In view of the above desirability, the amount of change ΔVve iscalculated in the following manner, which assures freedom of thecalculated amount of change ΔVve from the error Error between thecompensated wheel speed Vwmaxc and the estimated vehicle speed Vve, sothat the amount of change ΔVve is responsive to a decrease in thefriction coefficient μ within a time period of 0.25-0.5 sec, and to anincrease in the friction coefficient μ within a time period of 0.5-0.75sec. ##EQU6## where, Eps4u=0.4, Eps4d=-0.2

In the present embodiment, the portion of the computer 82 assigned toimplement the above calculation serves as a filter for filtering theestimated vehicle speed Vve.

The above method of calculation is an improvement over the basicsecond-order delay type smoothing method indicated below. ##EQU7##

The value Eps4u and Eps4d are set at 0.4 and -0.2, respectively, so thatthe estimated vehicle speed Vve deals with a decrease in the frictioncoefficient μ more quickly than an increase in the friction coefficientμ.

According to the above basic second-order delay type smoothing method,the amount of change ΔVve of the estimated vehicle speed immediatelyafter the commencement of anti-lock regulation of the brake pressures isinitially set at a value corresponding to a sufficiently high value(preferably higher than 0.6, more preferably higher than 0.8, and mostpreferably almost 1.0) of the friction coefficient μ, so as to eliminatea response delay of the estimated vehicle speed Vve with respect to anincrease in the friction coefficient. However, the method suffers from aproblem of excessive amounts of slip of the wheels immediately after thecommencement of anti-lock regulation of the brake pressures when thefriction coefficient μ is relatively low. In the present embodiment,this problem is solved by introducing the absolute value of the rearwheel speed difference Vwrdif so that the estimated vehicle speed Vve ismore responsive to a decrease in the friction coefficient.

Normally, the above solution permits adequate determination of theestimated vehicle speed Vve. When the absolute value of the rear wheelspeed difference Vwrdif is extremely large or small, the calculatedestimated vehicle speed Vve is not sufficiently responsive to a changein the rear wheel speed difference, leading to unsatisfactory accuracyof anti-lock regulation of the brake pressures. In the light of thisdrawback, it was proposed to improve the manner of determining theestimated vehicle speed Vve, by introducing values Tmp×4 and Tmp×2 aslearning amounts for increased response of the estimated vehicle speedVve, as indicated below. ##EQU8## where, Eps4U=0.4, Eps4d=-0.2

However, a further study revealed that the above manner of calculationof the estimated vehicle speed Vve is still unsatisfactory in itsresponse, due to retention of the error value Error of the same sign(error in the same direction) for a considerably long time, causingdeterioration of accuracy of the anti-lock brake pressure regulation.

To overcome the above drawback, the present embodiment uses a largelearning amount Tmp×8 to improve the response of the estimated vehiclespeed Vve, irrespective of an increase or a decrease in the frictioncoefficient μ, if the error value Error of the same sign is retained formore than a predetermined time 100 msec (=20×cycle time CYCT of 5 msec),as indicated above.

The estimated vehicle speed Vve thus generated by the generating means131 is used by the generating means 132 for calculating the referencewheel speed Vsn according to the following equation:

    Vsn=Vve-Ssn

where, Ssn represents a reference slip amount of the wheels and iscalculated according to the following equation:

    Ssn=A×Vve+B

It will be understood from the above equation that the value Ssn isproportional to the estimated vehicle speed Vve.

The thus obtained reference wheel speed Vsn is used for the front wheelFL or FR which is on the outer side with respect to the turning path ofthe vehicle. It is noted that the reference wheel speed Vsn is notnecessary for the outer rear wheel RL or RR, because this rear wheel isthe non-selected higher-speed rear wheel which serves as the speedmonitoring wheel as described above. For the inner front and rearwheels, however, the reference wheel speed Vsn as calculated accordingto the above equation Vsn=Vve-Ssn is modified according to the followingequation:

    vsn=Vsn-Vwfdif×K3

where, K3: compensating coefficient

While the constant K3 is theoretically 0.5, it is selected within arange of 0.25-0.375, since the use of the value 0.5 for the constant K3tends to cause an oscillatory phenomenon. In the present embodiment, theconstant K3 is set at 0.25.

It will be understood from the foregoing description of the presentembodiment wherein the constants K1, K2 and K3 are set at 0.25, 0.75 and0.25, respectively, that the reference wheel speed Vsn (estimatedvehicle speed Vve) is adjusted with respect to the maximum wheel speedVwmax, by an amount corresponding to 1/2 of the distance Ww between theright and left wheels, for the front wheel on the outer side of thevehicle turning path, and by an amount corresponding to 3/4 of thedistance Ww, for the front and rear wheels on the inner side of theturning path. However, the constants K1, K2 and K3 may be modified asneeded, for example, set at 0.25, 0.625 and 0.5, respectively, so thatthe reference wheel speed Vsn is adjusted with respect to the maximumwheel speed Vwmax, by an amount corresponding to 3/8 of the distance Wwfor the outer front wheel, and by an amount corresponding to 7/8 of thedistance Ww for the inner front and rear wheels.

Although the above adjustment is theoretically unnecessary for the outerwheels, the present embodiment is adapted to make the adjustment for theouter front wheel, so as to obtain the estimated vehicle speed slightlylower than the optimum level, for controlling the brake pressures forthe front wheels to be slightly higher than actually required, andcontrol the brake pressures for the rear wheels in the so-called"selectro-control fashion", that is, control the brake pressure for theouter rear wheel (higher-speed rear wheel or speed monitoring wheel) inthe same manner as the inner rear wheel (selected lower-speed rearwheel), so that the controlled brake pressures for the rear wheels arecomparatively lower than the optimum level.

Thus, by suitably determining the adjusting constants K1, K2, K3, thebrake pressures for the wheels can be regulated so as to cope with botha change (in particular, a decrease) in the friction coefficient μ ofthe road surface and turning of the vehicle (a change in the angularvelocity of the vehicle). The present embodiment eliminates theconventionally required means for and steps of detecting the frictioncoefficient μ below a given lower limit and the angular velocity above agiven upper limit, so as to suitably change the mode of controlling thebrake pressures depending upon the friction coefficient and the angularvelocity of the vehicle. The conventional control arrangement requirescomplicated control logics for changing the control mode, and suffersfrom unstable control and fluctuation of the brake pressures uponchanging of the control mode. The present embodiment is free from theseconventional drawbacks.

Conventionally, the reference wheel speed Vsn is calculated from theestimated vehicle speed Vve which is obtained by limiting the rate ofchange of the non-processed maximum wheel speed. In calculating thereference wheel speed Vsn, the disturbance value determined from theoccurrence frequency of abnormality in the wheel acceleration iscompared with a threshold value which is changed in steps, so that theslip amount of the wheel is adjusted in steps. In the presentembodiment, on the other hand, the estimated vehicle speed Vve isadjusted on the basis of the common external disturbance value Vn, andthe absolute values of the rear wheel speed difference Vwrdif and thefront wheel speed difference Vwfdif, before the estimated vehicle speedVve is filtered into the reference wheel speed Vsn. The pre-filteredestimated vehicle speed Vve is used for all the four wheels, while thepost-filtered estimated vehicle speed Vve, namely, the reference wheelspeed Vsn is used for only the inner front and rear wheels. The presentarrangement wherein the adjustment is sufficiently delayed is effectiveto reduce the tendency of oscillation of the brake pressures when theamount of adjustment of the estimated vehicle speed is large.

While the above description is given on the assumption that the fourwheels have the same tire diameter, the tire diameters of the individualwheels may be actually different from each other. In this respect, it isdesirable that the reference wheel speed Vsn for each wheel be adjusteddepending upon the tire diameter of the wheel, which may be obtainedfrom a difference of the speed of that wheel from the speeds of theother wheels when no brake is applied to the vehicle.

There will next be described the manner of calculation of the estimatedovershoot drop amount Vprev of each wheel speed. The overshoot dropamount Vprev of the wheel speed is an amount of drop of the wheel speeddue to 5 control overshoot, which occurs after commencement of reductionor decrease in the brake pressure.

The calculating means 134 calculates the estimated wheel speed dropamount Vprev due to the overshoot, upon commencement of reduction in thebrake pressure for each wheel, on the basis of a parameter or parametersrelating to or indicative of the road surface condition, for example, onthe basis of the brake pressure and the time duration of the brakepressure decrease, or the friction coefficient μ of the road surface, orthe friction coefficient μ and an external disturbance value or values.The thus calculated estimated overshoot drop amount Vprev is thereaftergradually reduced as the time passes.

In the calculating means 134, the estimated overshoot drop amount Vprevof the speed of each wheel is initially calculated according to thefollowing equation, on the basis of the friction coefficient μ of a dryasphalt road surface as a standard road surface, and the common externaldisturbance value Vn0 calculated by the calculating means 128.

Upon commencement of initial or subsequent brake pressure decrease:

    Vprev.sub.n =Vprev.sub.n-1 ×0.5+2.5+Vn0×0.25

After the commencement of brake pressure decrease:

    VPrev.sub.n =Vprev.sub.n-1 ×(1-1/16)-0.1

The calculating means 134 receives the common external disturbance valueVn0 from the calculating means 130 (although this is not shown in theblock diagram of FIG. 3.), so that the estimated overshoot drop amountVprev increases with an increase in the disturbance value Vn0.

As discussed below, the reduction or decrease in the brake pressure foreach wheel is commenced, in principle, when the speed Vw of the wheelfalls below the reference wheel speed Vsn. However, the wheel speed Vwcontinues to drop due to the control overshoot, even after thecommencement of decrease in the brake pressure in the brake cylinder 26,36, 46, 54, as indicated in FIG. 8. A given time after the commencementof the brake pressure decrease, the wheel speed Vw begins to rise. Theamount of the overshoot drop of the wheel speed varies depending uponthe specific braking condition. To cope with this variation, theconventional brake system is adapted to utilize the wheel acceleration(deceleration) value in determining the point of time at which the brakepressure decrease is terminated or the subsequent brake pressureincrease is commenced. But, the wheel acceleration is easily affected bythe external disturbance, and the conventional arrangement inevitablysuffers from insufficient accuracy of control of the brake pressure,when the external disturbance is considerably large. If the wheel speedand the wheel acceleration are both utilized to determine the point oftermination of the brake pressure decrease, the brake system requirescomplicated control logics.

In the light of the above drawback experienced in the prior art, thewheel acceleration is replaced by the estimated overshoot drop amountVprev, and a critical wheel speed (Vsn-Vprev) is obtained and used indetermining whether the brake pressure should be further decreased, orshould alternatively be increased. As indicated in FIG. 8, the estimatedovershoot drop amount Vprev (positive value) is calculated uponcommencement of the brake pressure decrease (when the wheel speed Vwfalls below the reference wheel speed Vsn), and the value Vprev issubsequently gradually reduced from the initial value.

Since the estimated overshoot drop amount Vprev is used as a parameterreflecting the tendency of an eventual rise of the wheel speed up towardthe reference wheel speed Vsn after the commencement of the brakepressure decrease, it is desirable that the overshoot drop amount Vprevchange almost following the actual wheel speed Vw, that is, the curve ofthe value Vprev is close to and substantially follows the curve of thewheel speed Vw. In practice, however, it is suffice that the curve ofthe estimated overshoot drop amount Vprev lies generally below theexpected curve of the actual wheel speed Vw which is lower than thereference wheel speed Vsn.

In view of the above need, the present embodiment is adapted toinitially set the estimated overshoot drop amount Vprev to aconsiderably large value upon commencement of the brake pressuredecrease, and thereafter gradually reduce the amount Vprev, as indicatedin FIG. 8. The curve Prev approximating the convex curve Vw takes theform of a sawtooth which represents an estimated initial overshoot dropof the wheel speed upon commencement of a brake pressure decrease, andan estimated gradual rise of the wheel speed as the time passes afterthe initial overshoot drop. The overshoot drop amount Vprev of the wheelspeed is represented by the distance between the sawtooth curve Prev anda line representative of the reference wheel speed Vsn, as indicated inFIG. 8. Although this is a simple arrangement to satisfy the above need,the method of setting the overshoot drop amount Vprev is not limited tothe specific form illustrated in FIG. 8, but may be modified as needed.For instance, the gradual reduction of the amount Vprev may take otherforms, and may be preceded by an initial gradual increase for a suitabletime period after the commencement of the brake pressure decrease.

Each brake pressure decrease is effected for a predetermined constanttime period T0. Upon termination of the brake pressure decrease orexpiration of the predetermined time period T0, the detected wheel speedVw (more precisely, near future wheel speed Vwf which will be describedin detail) is compared with the critical wheel speed (Vsn-Vprev). If thewheel speed Vw is higher than the critical wheel speed (Vsn-Vprev) asindicated in solid lines in FIG. 8, then an increase in the brakepressure is commenced. If the wheel speed Vw further drops below thecritical wheel speed (Vsn-Vprev) as indicated in dashed lines in FIG. 8,on the other hand, another brake pressure decrease is commenced, withthe overshoot drop amount Vprev being updated. This brake pressuredecrease is referred to as "subsequent brake pressure decrease". Thesubsequent brake pressure decrease is repeated until the wheel speed Vwrises above the critical wheel speed (Vsn-Vprev). Thus, a suitablenumber of repetition of the brake pressure decrease cycles are effectedto achieve anti-lock regulation of the brake pressure to an optimumlevel depending upon the specific braking condition.

If the friction coefficient μ of the road surface is suddenly loweredduring brake application to the vehicle, the actual wheel speed Vw isconsiderably lowered due to a relatively large amount of overshoot drop,with respect to the critical wheel speed (Vsn-Vprev), and the brakepressure decrease cycle is repeated a suitable number of times, asindicated in FIG. 9, whereby the brake pressure is lowered sufficientlyto a level that meets the lowed friction coefficient μ.

If the present brake pressure regulation using the estimated overshootdrop amount Vprev or the critical wheel speed (Vsn-Vprev) is effectedtogether with the well known technique wherein the brake pressure isheld for a suitable time between the adjacent pressure decrease cycles,the brake pressure can be adequately controlled even during a vehiclerunning on a bad road surface having a relatively high frictioncoefficient μ.

While the above description relates to the anti-lock brake pressureregulation in a tentative case wherein no external disturbances exist,the external disturbances which actually exist to some extent may lowerthe actual wheel speed Vw to a level lower than the critical wheel speed(Vsn-Vprev). In this case, the brake pressure is unnecessarily lowereddue to the subsequent pressure decrease cycle or cycles. In view of thisdrawback, the initial estimated overshoot drop amount Vprev for theinitial brake pressure decrease is determined so as to increase with anincrease in the common external disturbance value Vn0.

The generating means 122 calculates a present speed error Hensa of eachof the front wheels FL, FR and selected lower-speed rear wheel RL or RR,on the basis of the thus obtained critical wheel speed (Vsn-Vprev), theindividual external disturbance values Vn1, and the wheel speed Vw andits first and second relative wheel speed change amounts ΔVw1 and ΔVw2which have been calculated by the calculating means 120 as describedabove. The wheel speed error Hensa is used to determine whether aninitial brake pressure decrease should be commenced.

Theoretically, the wheel speed error Hensa can be obtained bysubtracting the critical wheel speed (Vsn-Vprev) from the wheel speed Vwas adjusted by the external disturbance value Vn1. In the presentembodiment, however, the wheel speed error Hensa is calculated in thefollowing manner.

To begin with, a first error value Hensa1 is calculated according to thefollowing equations, on the basis of the wheel speed Vw, externaldisturbance value Vn1, and critical wheel speed (Vsn-Vprev):

    Hensa1=(Vw+Vn1)-(Vsn-Vprev)

    Hensa1=MIN(Hensa1, Limit)

Then, a second error value Hensa2 is calculated according to thefollowing equations, on the basis of the first error value Hensa1, firstrelative wheel speed change amount ΔVw1, and external disturbance valueVn1: ##EQU9##

Finally, the wheel speed error Hensa is calculated according to thefollowing equation, on the basis of the thus calculated first and secondwheel speed errors Hensa1 and Hensa2:

    Hensa=MAX{Hensa1, (Hensa1+Hensa2)/2}

According to the above calculation, the first relative wheel speedchange amount ΔVw1 serves to reduce the wheel speed error Hensaimmediately before commencement of an initial brake pressure decrease,for thereby starting the brake pressure decrease at a relatively earlypoint of time, while the estimated overshoot drop amount Vprev serves toincrease the wheel speed error Hensa after termination of the brakepressure decrease, thereby making it difficult for a subsequent brakepressure decrease to take place. Further, the second relative wheelspeed change amount ΔVw2 serves to inhibit a decrease in the brakepressure after the wheel speed Vw rises above the critical point(Vsn-Vprev).

The ABS actuator 78 of the anti-lock brake system may be a three-modetype having a pressure-increase mode, a pressure-hold mode and apressure-decrease mode, or a rapid/slow increase type in which the brakepressure may be increased either rapidly or slowly. Where the brakesystem is provided with such type of ABS actuator, the positive value ofthe wheel speed error Hensa may be used to increase the brake pressureat a rate which increases with the value of the wheel speed error Hensa.

The reference wheel speed if obtained by adding the wheel accelerationcomponent (amount of change of the wheel speed) to the wheel speed isundesirably influenced by external disturbances due to a bad roadsurface condition. However, it was found out that the brake system wouldbe capable of suitably dealing with both good and bad conditions of theroad surface if the wheel acceleration component (first and secondamounts of change ΔVw1, ΔVw2 of the relative wheel speed Vwv) iscompressed as the road surface condition deteriorates.

It was found that since the second relative wheel speed change amountΔVw2 is equivalent to an integral of the last eight values of the firstrelative wheel speed change amount ΔVw1, the substitution of ΔVw2/2 forΔVw1×4 is effective to suitably deal with a bad road surface condition,but unfavorably results in inaccurate control of the brake pressures fora good surface condition. This means that weighting the first and secondrelative wheel speed change amounts ΔVw1 and ΔVw2 as needed improves theaccuracy of control of the brake pressures. In other words, the accuracyor adequacy of the anti-lock brake pressure control can be improved byusing as a control parameter a future wheel speed error Hensaf which isobtained from the first and second relative wheel speed change amountsΔVw1 and ΔVw2.

In the present embodiment, the future wheel speed error Hensaf iscalculated according to the following equation, on the basis of theindividual external disturbance value Vn1 and the second relative wheelspeed change amount ΔVw2:

    Hensaf=Hensa+(ΔVw2+Vn1)×20 msec/40 msec

Since the second relative wheel speed change amount ΔVw2 is an amount ofchange of the relative wheel speed Vvw with respect to the referencewheel speed Vsn, as explained above, the future wheel speed error Hensafis a sum of the wheel speed error Hensa and an estimated amount ofchange ΔVw2/2 of the wheel speed Vw (relative to the reference wheelspeed Vsn) during a future period of 20 msec, as indicated in the graphof FIG. 10.

Then, the final value of the future wheel speed error Hensaf is obtainedaccording to the following equation:

    Hensaf=MAX(Hensa, Hensaf)

According to the above equation, the wheel speed error Hensa is used asthe future wheel speed error Hensaf if the calculated value Hensaf issmaller than the wheel speed error Hensa. The final value of the futurewheel speed error Hensaf is used to determine the point of time at whicha subsequent brake pressure decrease or a brake pressure increase iscommenced.

The above arrangement makes it possible to shorten the required brakingdistance of the vehicle, by retarding the brake pressure decrease andadvancing the brake pressure increase so as to assure a sufficient brakeforce to be exerted on the wheel.

On the basis of the wheel speed error Hensa and the future wheel speederror Hensaf, and the data indicative of the selected lower-speed wheelRL or RR received from the determining means 124, the determining means136 determines the point of time at which the brake pressure decrease orincrease is commenced.

In principle, an initial or first brake pressure decrease is commencedwhen the wheel speed error Hensa becomes negative. The brake pressuredecrease continues for the predetermined time duration T0. If the futurewheel speed error Hensaf remains negative upon expiration of the timeT0, another or subsequent brake pressure decrease cycle is effected. Ifthe value Hensaf at that moment has been raised to a positive valuewithin the time duration T0, a brake pressure increase cycle iscommenced.

As the time duration T0 is determined assuming that the road surface hasa relatively high friction coefficient μ, the initial or first brakepressure decrease where the friction coefficient is relatively highresults in a sufficient amount of rise of the wheel speed after theovershoot drop, leading to a positive value of the future wheel speederror Hensaf. Where the friction coefficient is relatively low, on theother hand, the initial brake pressure decrease may be insufficient forthe future wheel speed error Hensaf to become positive, namely, thevalue Hensaf remains negative, whereby a subsequent brake pressuredecrease is effected. Thus, a suitable number of brake pressure decreasecycles are repeatedly implemented each for the predetermined timeduration T0, where the friction coefficient is relatively low, so thatthe total amount of brake pressure decrease is sufficient to deal withthe relatively low friction coefficient.

The points of time at which the brake pressure decrease or increase forthe front wheels FL, FR is commenced are determined independently ofeach other. For the rear wheels RL, RR, however, the points of time ofcommencement of the brake pressure decrease or increase are determinedin the so-called "selectro-control fashion", in which the points of timeare determined on the values Hensa and Hensaf of the selectedlower-speed rear wheel RL or RR which is supposed to have a large amountof slip on the road surface. But, the points of time at which the brakepressure decrease for the rear wheels RL, RR is terminated are madedifferent. More specifically, the point of time at which the brakepressure decrease for the non-selected higher-speed rear wheel (i.e.,speed monitoring wheel discussed above) is terminated is delayed by apredetermined short time length (e.g., 1-2 msec) with respect to thatfor the lower-speed rear wheel, so that the brake pressure for the speedmonitoring rear wheel is made lower than that for the other orlower-speed rear wheel, in an attempt to purposely cause the speedmonitoring wheel to have the maximum wheel speed Vwmax close to theactual wheel speed.

As indicated above, one of the rear wheels RL and RR which has a lowerspeed is used as the selected rear wheel whose values Hensa and Hensafare used for determining the points of time of commencement of the brakepressure decrease and increase, and the other rear wheel having a higherspeed is used as the speed monitoring wheel. As a result, the brakeforce of the speed monitoring wheel is controlled as indicated by aclosed loop H1 in FIG. 11, while that of the selected lower-speed rearwheel is controlled as indicated by a closed loop H2 in FIG. 11.

On the other hand, the brake forces of the front wheels FL, FR arecontrolled as indicated by a closed loop H3 in FIG. 12, so that theaccuracy of control of the brake pressures is improved to reduce anamount of variation in the slip amount of the front wheels, therebyeffectively shortening the required braking distance of the vehicle.

It will be understood from the foregoing description of the presentembodiment of this invention that the wheel speed sensors 100, 102, 104,106, and the calculating means 120 of the electronic control device 80assigned to process the output signals of those wheel speed sensorsconstitute means for obtaining the speeds of the wheels. Further, thedetermining means 126, calculating means 128 and 130 and generatingmeans 131 constitute means for obtaining the vehicle speed, while thecalculating means 120 also serves as means for obtaining the first andsecond relative wheel speed changes ΔVw1 (or ΔVwx1) and ΔVw2. It is alsonoted that the generating means 122 and 132, determining means 136 andthe ABS actuator 78 constitute pressure regulating means for regulatingthe brake pressures in the wheel brake cylinders 26, 36, 46, 54.

In the present embodiment, the common external disturbance value Vn0,individual external disturbance values Vn1, and absolute values of thefront wheel speed difference Vwfdif and rear wheel speed differenceVwrdif are used to calculate the wheel speed error Hensa and the futurewheel speed error Hensaf, so that the brake pressures are suitablycontrolled depending upon the friction coefficient μ and waviness orbumpiness of the road surface, degree of turning of the vehicle andother running conditions of the vehicle. The value Vn0 and the otherparameters used for obtaining the values Hensa and Hensaf are allcontinuously variable, contrary to the conventionally used controlparameters which change in steps depending upon the running conditionsof the vehicle indicated above. Accordingly, the arrangement accordingto the present embodiment is capable of avoiding a considerable controlerror which would arise from a non-continuous step-up or step-downchange of the control parameters. In this respect, too, the presentbrake system assures improved accuracy of anti-lock brake pressurecontrol.

It will also be understood that the common external disturbance valueVn0, for example, may be used for compensating any one of the maximumwheel speed Vwmax, estimated wheel speed Vve, reference wheel speed Vsnand wheel speed error Hensa, with substantially the same result obtainedby the compensation. Therefore, there is a large degree of freedom indetermining the process steps in which the above-indicated values areused. In this respect, the timing of use of those values is not limitedto that of the illustrated embodiment.

Moreover, the present embodiment permits highly accurate regulation ofthe brake pressures by a rapid decrease and a slow increase of thepressure, which is conventionally considered difficult during running ofthe vehicle on the road surface having a comparatively low frictioncoefficient μ or at a comparatively low speed. That is, the conventionaldifficulty is overcome by the following features: suitably smoothing thewheel speed Vw and estimated vehicle speed Vve; calculating theestimated wheel speed Vext by extrapolation; introducing the overshootdrop amount Prev of the wheel speed (critical wheel speed Vsn-Vprev);and introducing the near future wheel speed Vwf, as well as by givingdifferent roles to the rear left and right wheels RL, RR and determiningthe reference wheel speed Vsn on the basis of the continuously variablecontrol values.

Any one of the above features may be used alone, or the features may beused in combination. In any case, an appropriate advantage may beobtained.

In the illustrated embodiment, each of the four wheels FL, FR, RL, RR isprovided with two solenoid-operated valves for increasing and decreasingthe brake pressure. However, other valve arrangements are possible forcontrolling the brake pressures for the wheels. For instance, each wheelmay be provided with a solenoid-operated directional control valvehaving a pressure-increase position, a pressure-hold position and apressure-decrease position, or a combination of a solenoid-operatedvalve having a pressure-increase position and a pressure-decreaseposition and a flow control valve.

Although the illustrated embodiment is adapted for use on an FF vehicle(front-engine front-drive vehicle), the principle of the presentinvention is equally applicable to an FR vehicle (front-enginerear-drive vehicle) and a 4-WD vehicle (four-wheel-drive vehicle). Whenthe present invention is applied to a brake system for the FR or 4-WDvehicle, suitable modifications should be made so as to meet thespecific operating condition of the vehicle, namely, application ofdrive forces to the rear wheels on the FR vehicle, and application ofdrive forces to all the four wheels and mutual influences of the speedsof the four wheels through a differential gear on the 4-WD vehicle.

In the illustrated embodiment, each wheel speed sensor includes a rotorhaving multiple teeth equally spaced from each other along a circle, andan electromagnetic pick-up which is opposed to the teeth of the rotorand adapted to electromagnetically detect the passage of each tooth ofthe rotor. The AC output signal of the electromagnetic pick-up isprocessed to calculate the average wheel speed in the form ofnon-processed wheel speed Vxa on the basis of a time interval betweentwo intermediate points each of which is intermediate between adjacenttwo points at which the level of the output signal rises above and fallsbelow a threshold value, namely, intermediate between adjacent twozero-crossing points which define the width of each tooth of the rotoror each groove between adjacent two teeth of the rotor. Thenon-processed estimated wheel speed Vext at the present sampling pointis calculated on the basis of a plurality of successive values of thenon-processed wheel speed Vxa which have been obtained prior to thepresent sampling point.

The wheel speed sensor including the teethed rotor and theelectromagnetic pick-up as described above is widely used. In thisconnection, it is noted that the time interval between a pair ofzero-crossing points of the output signal of the electromagnetic pick-upis not necessarily the same as that between the adjacent pair ofzero-crossing points. In other words, the time interval between thezero-crossing points corresponding to the opposite edges of a tooth ofthe rotor usually differs from that between the zero-crossing pointscorresponding to the opposite edges of a groove of the rotor. Further,these time intervals may vary due to eccentricity of the rotor withrespect to the pick-up. However, the time interval (indicated at DVT inFIG. 5) between two points each intermediate between the edges of atooth or a groove of the rotor is constant, irrespective of a differencebetween the time interval corresponding to the width of the rotor toothand the time interval corresponding to the width of the rotor groove, aslong as the wheel (rotor attached to the wheel) is rotating at aconstant speed. Accordingly, the present embodiment assures highaccuracy of calculation of the average wheel speed or non-processedwheel speed Vxa and the estimated wheel speed Vext at the presentsampling point.

If the time interval between any pair of adjacent zero-crossing pointsof the AC output signal of the wheel speed sensor is considered to beconstant, the average wheel speed Vxa may be obtained based on the timeinterval between these adjacent zero-crossing points. If the actualwheel speed linearly changes, the calculated average wheel speed Vxa isthe wheel speed at the point of time intermediate between those adjacentzero-crossing points.

In the above case, it is desirable to calculate the average wheel speedVxa on the basis of the adjacent zero-crossing points which are the lasttwo zero-crossing points immediately prior to the present samplingpoint. However, the average wheel speed Vxa may be obtained on the basisof last three or more successive zero-crossing points immediately priorto the present sampling point.

The estimated wheel speed Vext at the present sampling point is obtainedby extrapolation on the basis of two or more values of the average wheelspeed. The simplest way is to calculate the estimated wheel speed Vextaccording to an appropriate first-order equation, on the basis of thetwo values of the average wheel speed, which consist of the presentvalue Vxa and the last value VxaL, as in the illustrated embodiment.However, it is possible to calculate the estimated wheel speed Vextaccording to a first-order or higher-order equation which includes thethree or more values of the average wheel speed which include thepresent value Vxa.

In the illustrated embodiment, the estimated wheel speed Vext at thepresent sampling point is calculated at the predetermined cycle timeCYCT (at the predetermined sampling interval), and the amount of changeof the wheel speed during a period equal to a multiple of the cyclingtime is calculated on the basis of the obtained two or more values ofthe estimated wheel speed Vext. This arrangement permits calculation ofthe amount of change of the wheel speed at the predetermined cycle time,and is effective to reduce a delay in the detection of the amount ofchange of the wheel speed. Since the cycle time for calculating theamount of change of the wheel speed is made equal to the cycle time atwhich the anti-lock brake pressure control cycle is repeated, eachcontrol cycle is implemented with the updated change amount of the wheelspeed.

However, the cycle time for calculating or updating the amount of changeof the wheel speed need not be equal to the cycle time of the anti-lockbrake pressure control.

In the illustrated embodiment, the locking of each wheel is detectedwhen any EDGE signal corresponding to an edge of a tooth or groove ofthe rotor of the wheel speed sensor is not generated for more than apredetermined length of time. In this case, the estimated wheel speedVext and the first relative wheel speed change amount ΔVw1 are reset tozero. However, it is possible that the locking of the wheel is detectedwhen the rear wheel speed difference Vwrdif exceeds a predeterminedupper limit. In this case, the reference wheel speed Vsn is raised toeliminate the wheel locking. One of these two alternative arrangementsmay be used, or both of these alternatives may be employed.

The illustrated embodiment is adapted to obtain the second relativewheel speed change amount ΔVw2 according to the equation ΔVw2_(n)=ΔVw2_(n-1) ×7/8+ΔVw1_(n). In this respect, it is considered that thesecond relative wheel speed change amount ΔVw2 upon commencement of abrake pressure decrease increases as the road surface conditiondeteriorates. Accordingly, it is possible to replace the first andsecond relative wheel speed change amounts ΔVw1 and ΔVw2 withcorresponding first and second compensated relative wheel speed changeamounts ΔVw1c and ΔVw2c, which are calculated according to the followingequations, on the basis of the individual external disturbance value Vn1obtained from the second relative wheel speed change amount ΔVw2:

    ΔVw1c=ΔVw1+Vn1/8

    ΔVw2c=ΔVw2+Vn1

While the illustrated embodiment is adapted to gradually reduce theabsolute amount of the estimated overshoot drop amount Vprev of thewheel speed, irrespectively of the current vehicle speed (estimatedvehicle speed Vve). This arrangement tends to relatively easily causelocking of the wheel when the vehicle speed is considerably lowered.

To avoid the above drawback, it is effective to increase the rate ofreduction of the estimated overshoot drop amount Vprev as the estimatedvehicle speed is lowered, or use a relatively high rate of reduction ofthe value Vprev when the estimated vehicle speed Vve is not higher thana given threshold level, and a relatively low rate of reduction of thevalue Vprev when the estimated vehicle speed Vve is higher than thethreshold level.

The illustrated embodiment is arranged such that the point of time atwhich an initial brake pressure decrease is commenced is determined onthe basis of the present wheel speed Vw, while the points of time atwhich a subsequent brake pressure decrease or a brake pressure increaseis commenced are determined on the basis of the near future wheel speedVwf. It is possible, however, to use the wheel speed Vw (present wheelspeed error Hensa) for the commencement of only an initial brakepressure decrease cycle immediately after the commencement of ananti-lock brake pressure control operation, and use the near futurewheel speed Vwf (future wheel speed error Hensaf) for the commencementof the other brake pressure decrease cycles.

In consideration of a tendency of some delay of an actual brake pressuredecrease with respect to the moment of generation of a pressure-decreasecommand, it is also possible to always use the near future wheel speedVwf for determining the point of time of commencement of any brakepressure decrease cycle.

Described more specifically, the present wheel speed Vw used as a majorcontrol parameter is replaced by the near future wheel speed Vwf as themajor control parameter, for example, near future wheel speed Vwf20 uponexpiration of 20 msec from the present time. In one example, the nearfuture wheel speed Vwf20 is used as the major control parameter, and thepresent wheel speed Vw and another near future wheel speed Vwf40 (wheelspeed 40 msec after the present time) are used as supplemental controlparameters, as indicated by the following equations:

    Tmp=MAX(Vw, Vwf20)

    Vwf=MIN(Tmp, Vw+ΔV, Vwf40+ΔV)

The above arrangement causes a brake pressure decrease to be commencedif the present wheel speed Vw or the near future wheel speed Vwf40 hasbeen lowered by a predetermined amount ΔV or more. For instance, theamount ΔV may be set at 1 km/hr.

It is also possible that the point of time at which an initial brakepressure decrease is commended is determined by a wheel speed Vwf at arelatively near future point of time, while the point of time at which asubsequent brake pressure decrease or a brake pressure increase iscommenced is determined by a wheel speed Vwf at a point of timesubsequent to the above-indicated relatively near future point. Further,it is possible that the point of time of commencement of a slow brakepressure increase or decrease or a brake pressure hold is determined bya near future wheel speed Vwf (future wheel speed error Hensaf) which isdifferent from a near future wheel speed Vwf used for determining thepoint of time of commencement of a rapid brake pressure decrease orincrease.

For instance, near future wheel speed error values Hensaf at respectivefuture points 5 msec and 10 msec after the present sampling point,namely, near future wheel speed error values Hensaf05 and Hensaf10 arecalculated according to the following equations:

    Hensaf05=Hensa+(ΔVw1+Vn1×5 msec/40 msec)

    Hensaf10=Hensa+(ΔVw1+Vn1×5 msec/40 msec)×2

In the illustrated embodiment, a brake pressure increase will follow abrake pressure decrease of a predetermined time duration, unless thefuture wheel speed error Hensaf has changed to a negative value duringthe brake pressure decrease cycle. This arrangement eliminates a need ofdetermining the time duration of the brake pressure decrease dependingupon the road surface condition and the vehicle running condition,thereby providing an advantage of simplified brake pressure controllogics. However, the time duration of the brake pressure decrease may bechanged depending upon the road surface and vehicle running conditions.

For instance, it is appreciated to increase the time duration of thebrake pressure decrease with a decrease in the absolute value of theamount of change ΔVve of the estimated vehicle speed Vve, since thebrake pressure and the friction coefficient μ of the road surfacedecrease with a decrease in that absolute value |ΔVve|.

The illustrated embodiment is adapted such that a brake pressuredecrease is effected when the present wheel speed error Hensa or futurewheel speed error Hensaf is a negative value. This arrangement is notessential. Generally, a brake pressure decrease is effected when thevalue Hensa or Hensaf becomes smaller than a predetermined threshold.

If the above threshold is a positive value, the brake pressure decreaseoccurs at a relatively early point of time, and it is thereforedesirable that the duration of the brake pressure decrease be relativelyshort.

In the illustrated embodiment, the determination of a need of commencinga brake pressure decrease is effected on the basis of the referencewheel speed Vsn (=Vve-Ssn), assuming that the reference wheel slipamount Ssn is constant, irrespective of whether the brake pressuredecrease occurs during an initial period following the start of ananti-lock brake pressure control operation (ABS operation) or anintermediate period following the initial period. However, the referencewheel slip amount Ssn may be variable. For instance, the reference wheelslip amount Ssn is comparatively large for an initial period of 630 msecafter the start of the ABS operation, and is comparatively small for thefollowing period. That is, the reference wheel slip amount Ssn may bereduced in steps as the time passes after the start of the ABSoperation. Alternatively, the reference wheel slip amount Ssn may begradually or continuously reduced as the ABS operation proceeds. Wherethe reference wheel slip amount Ssn used to determine the referencewheel speed Vsn is variable (reduced in steps or continuously) asindicated above, it is preferred to shorten the time duration of eachbrake pressure decrease with a decrease in the reference wheel slipamount Ssn.

According to the above modified arrangement, the amount of slip or theamount of change of the wheel speed is reduced during intermediate andterminal periods of the ABS operation, whereby the stability of thebrake pressure control is enhanced. Since the past external disturbancevalues Vn0, Vn1 are stored and subsequently used for calculating thepresent wheel speed error Hensa, the reference wheel slip amount Ssnshould be set at a comparatively large value during the initial periodof the ABS operation, but may be reduced after the number of the storeddisturbance values Vn0, Vn1 has increased to a considerable value.

For the non-selected higher-speed rear wheel to be able to effectivelyserve as the speed monitoring wheel, the brake pressure for thehigher-speed rear wheel is made lower than that for the selectedlower-speed rear wheel. To this end, the duration of a brake pressuredecrease for the non-selected higher-speed rear wheel is made longerthan a predetermined suitable level or a level determined depending uponthe road surface and vehicle running conditions. Conversely, theduration of a brake pressure increase for the higher-speed rear wheelmay be shortened. Alternatively, the duration of a brake pressuredecrease or increase for the selected lower-speed rear wheel may besuitably adjusted so as to lower the brake pressure for the higher-speedrear wheel with respect to that for the lower-speed rear wheel. Further,the durations of the brake pressure decrease or increase for the tworear wheels may be suitably adjusted.

Thus, the brake pressure for one of the lower-speed and higher-speedrear wheels is controlled to an optimum level, while the brake pressurefor the other rear wheel is lower or higher than the optimum level, oralternatively, the brake pressures for the two rear wheels are lower andhigher than the optimum level, respectively.

It is to be understood that the present invention may be embodied withvarious other changes, modifications and improvements, which may occurto those skilled in the art, in the light of the foregoing teachings.

What is claimed is:
 1. An apparatus for preventing excessive slipping ofa wheel of a motor vehicle, said apparatus comprising:pressureregulating means for regulating a brake force for braking the wheel;wheel speed obtaining means for obtaining the rotating speed of thewheel; vehicle speed obtaining means for obtaining a running speed ofthe vehicle; relative speed change obtaining means for obtaining, as akind of said amount of change of the rotating speed of the wheel, arelative wheel speed change amount which corresponds to an amount ofchange of a difference between the speeds of the wheel and the vehicleobtained by said wheel speed obtaining means and said vehicle speedobtaining means, respectively; and controlling means for controllingsaid pressure regulating means in accordance with at least said relativewheel speed change amount.
 2. An apparatus according to claim 1, whereinsaid wheel speed obtaining means includes:a wheel speed sensor whichgenerates an output signal whose frequency is proportional to therotating speed of the wheel; and wheel speed calculating means forcalculating the rotating speed of the wheel on the basis of said outputsignal generated by the wheel speed sensor.
 3. An apparatus according toclaim 2, wherein said wheel speed calculating means includes:a pulsesignal generating circuit for generating a pulse signal which hasalternate rises and falls when a magnitude of said output signal of saidwheel speed sensor crosses a predetermined level in opposite directions,respectively; an edge signal generating circuit for generating edgesignals corresponding to said rises and falls of said pulse signal; andaverage wheel speed calculating means for obtaining a plurality ofintermediate points of time each of which is intermediate betweenmoments of generation of adjacent two edge signals corresponding toadjacent rise and fall of said pulse signal, and calculating an averagespeed of the wheel during a time period between each pair of saidintermediate points of time, on the basis of said time period and thenumber of said edge signals generated during said time period.
 4. Anapparatus according to claim 3, wherein said wheel speed calculatingmeans further includes extrapolating means for calculating byextrapolation an estimated speed of the wheel at a sampling pointfollowing a moment of generation of a last one of said edge signals, onthe basis of a plurality of values of said average speed of the wheelobtained by said average wheel speed calculating means.
 5. An apparatusaccording to claim 1, wherein said relative speed change obtaining meansincludes smoothing means for obtaining a smoothed relative wheel speedchange amount by smoothing said relative wheel speed change amount. 6.An apparatus according to claim 5, wherein said smoothing meanscomprises a digital filter for obtaining said smoothed relative wheelspeed change amount by digital smoothing of said relative wheel speedchange amount.
 7. An apparatus according to claim 6, wherein saiddigital filter includes:a first digital filter for smoothing saidrelative wheel speed change amount to obtain a first relative wheelspeed change amount as said smoothed relative wheel speed change amount;and a second digital filter for smoothing said first relative wheelspeed change amount to obtain a second relative wheel speed changeamount as said smoothed relative wheel speed change amount.
 8. Anapparatus according to claim 5, wherein said smoothing means comprises:afirst digital filter for smoothing said relative wheel speed changeamount to obtain a non-compressed first relative wheel speed changeamount as said smoothed relative wheel speed change amount; andcompressing means for compressing said non-compressed first relativewheel speed change amount to obtain a compressed first relative wheelspeed change amount as said smoothed relative wheel speed change amount,said compressing means including at least one of positive compressingmeans for reducing an absolute value of said non-compressed firstrelative wheel speed change amount to obtain said compressed firstrelative wheel speed change amount when said non-compressed firstrelative wheel speed change amount is larger than a predeterminedpositive value, and negative compressing means for reducing the absolutevalue of said non-compressed first relative wheel speed change amount toobtain said compressed first relative wheel speed change amount whensaid non-compressed first relative wheel speed change amount is smallerthan a predetermined first negative value.
 9. An apparatus according toclaim 8, wherein said compressing means comprises at least said negativecompressing means, and said smoothing means further comprises means fordisabling said negative compressing means when said non-compressed firstrelative wheel speed change amount is smaller than a predeterminedsecond negative value smaller than said first negative value.
 10. Anapparatus according to claim 8, wherein said smoothing means furthercomprises a second digital filter for smoothing said compressed firstrelative wheel speed change amount obtained by said compressing means,to obtain a second relative wheel speed change amount as said smoothedrelative wheel speed change amount.
 11. An apparatus according to claim5, wherein said smoothing means comprises at least one of positivecompressing means for reducing an absolute value of said relative wheelspeed change amount to obtain a compressed relative wheel speed changeamount when said relative wheel speed change amount is larger than apredetermined positive value, and negative compressing means forreducing the absolute value of said relative wheel speed change amountto obtain said compressed relative wheel speed change amount when saidrelative wheel speed change amount is smaller than a predeterminednegative value.
 12. An apparatus according to claim 1, wherein saidmotor vehicle has a plurality of wheels, and said vehicle speedobtaining means comprises vehicle speed estimating means for obtainingan estimated vehicle speed on the basis of a highest wheel speed whichis a highest one of the rotating speeds of said plurality of wheels. 13.An apparatus according to claim 12, wherein said vehicle speedestimating means includes means for limiting at least one of anincreasing rate and a decreasing rate of said highest wheel speed. 14.An apparatus according to claim 12, wherein said vehicle speedestimating means includes at least one of: first adjusting means forreducing said highest wheel speed with an increase in an externaldisturbance value which is common to all of said plurality of wheels;second adjusting means for increasing said highest wheel speed with adecrease in a friction coefficient of a road surface on which thevehicle is running; and third adjusting means for reducing said highestwheel speed with an increase in a degree of turning of said vehicle. 15.An apparatus according to claim 14, wherein said vehicle speedestimating means includes smoothing means for smoothing said highestwheel speed as adjusted by at least one of said first, second and thirdadjusting means, to obtain said estimated vehicle speed.
 16. Anapparatus according to claim 15, wherein said smoothing means includesfirst integrating means for obtaining a first integral by integrating anerror between said estimated vehicle speed and said highest wheel speedas adjusted by at least one of said first, second and third adjustingmeans, and second integrating means for obtaining a final estimatedvehicle speed by integrating said first integral.
 17. An apparatusaccording to claim 15, wherein said controlling means comprisesanti-lock control means for controlling said pressure regulating meansto regulate the brake force for braking said wheel so as to preventexcessive slipping of said wheel on a road surface upon braking of saidvehicle, and wherein said vehicle speed estimating means includes saidsecond adjusting means, said smoothing means comprising means forsetting an amount of change of said estimated vehicle speed uponcommencement of an operation of said anti-lock control means, to a valuecorresponding to a friction coefficient of said road surface which ishigher than 0.6.
 18. An apparatus according to claim 15, wherein saidsmoothing means comprises means for smoothing said highest wheel speedto obtain said estimated vehicle speed such that said estimated vehicleis more responsive to said highest wheel speed when said frictioncoefficient of the road surface decreases, than when said frictioncoefficient increases.
 19. An apparatus according to claim 15, whereinsaid smoothing means comprises response adjusting means for causing aneasier change of said estimated vehicle speed in at least one of firstand second cases where said friction coefficient of the road surface ishigher and lower than respective upper and lower limits, respectively,than in cases other than said first and second cases.
 20. An apparatusaccording to claim 15, wherein said smoothing means comprises responseadjusting means for causing an easier change of said estimated vehiclespeed in at least one of first and second cases where an error betweensaid estimated vehicle speed and said highest wheel speed as adjusted byat least one of said first, second and third adjusting means is heldpositive and negative for more than a first and a second predeterminedtime, respectively, than in cases other than said first and secondcases.
 21. An apparatus according to claim 7, wherein said motor vehiclehas a plurality of wheels whose brake pressures are regulated by saidpressure regulating means, and said vehicle speed obtaining meanscomprises vehicle speed estimating means for obtaining an estimatedvehicle speed on the basis of a highest wheel speed which is a highestone of the rotating speed of said plurality of wheels, and wherein saidvehicle speed estimating means includes at least one of: first adjustingmeans for reducing said highest wheel speed with an increase in anexternal disturbance value which is common to all of said plurality ofwheels; second adjusting means for increasing said highest wheel speedwith a decrease in a friction coefficient of a road surface on which thevehicle is running; and third adjusting means for reducing said highestwheel speed with an increase in a degree of turning of said vehicle. 22.An apparatus according to claim 21, wherein said first adjusting meanscomprises common disturbance obtaining means for obtaining said externaldisturbance value on the basis of an absolute value of a smallestnegative value of said second relative wheel speed change amounts of thewheels whose brake pressures are increasing.
 23. An apparatus accordingto claim 22, wherein said first adjusting means further comprises meansfor disabling said common disturbance obtaining means for apredetermined time duration after commencement of operation of saidpressure regulating means to regulate said brake pressures for thewheels.
 24. An apparatus according to claim 22, wherein said commondisturbance obtaining means comprises means for limiting a decreasingrate of said external disturbance value while the absolute value of saidsmallest negative value is decreasing.
 25. An apparatus according toclaim 21, wherein said plurality of wheels include a rear right wheeland a rear left wheel, and said second adjusting meanscomprises:pressure-difference generating means for generating a pressuredifference between a first rear brake pressure for one of said rearright and left wheels whose rotating speed is higher than the other rearwheel, and a second rear brake pressure for said other rear wheel, suchthat said first rear brake pressure is lower than said second rear brakepressure; and means for increasing said highest wheel speed with anincrease in a rear wheel speed difference between the rotating speeds ofsaid rear right and left wheels.
 26. An apparatus according to claim 21,wherein said plurality of wheels include a front right wheel and a frontleft wheel, and said third adjusting means comprises means for reducingsaid highest wheel speed with an increase in a front wheel speeddifference between the rotating speeds of said front right and leftwheels.
 27. An apparatus according to claim 1, wherein said wheel speedobtaining means comprises:vehicle speed change calculating means forcalculating an estimated vehicle speed change amount which is adifference between two values of the running speed of the vehicle; andmeans for calculating a present value of the rotating speed of thewheel, by adding said estimated vehicle speed change amount and saidrelative wheel speed change amount obtained by said relative speedchange obtaining means, to a last value of the rotating speed of thewheel.
 28. An apparatus according to claim 27, wherein said pressureregulating means comprises:generating means for generating a referencespeed of the wheel on the basis of the running speed of the vehicleobtained by said vehicle speed obtaining means; and commanding means forgenerating a control command for regulating said brake force, on thebasis of a difference between said present value of the rotating speedof the wheel and said reference speed of the wheel.
 29. An apparatusaccording to claim 1, wherein said controlling means comprises anti-lockcontrol means for controlling said pressure regulating means to regulatethe brake force for braking said wheel so as to prevent excessiveslipping of said wheel on a road surface upon braking of said vehicle.